the conditional expectation of a random variable X is the weighted average of all its possible outcomes x, weighted by the marginal probability of those outcomes occurring
1. T
2. F
Answers
The statement that the conditional expectation of a random variable X is the weighted average of all its possible outcomes x, weighted by the marginal probability of those outcomes occurring, is false.
The statement is false. The conditional expectation of a random variable X is not calculated by taking the weighted average of all possible outcomes of X, weighted by the marginal probability of those outcomes occurring. Instead, it is calculated using the concept of conditional probability and involves taking the average of the possible values of X given a certain condition or event.
The conditional expectation of a random variable X given an event A is denoted as E(X | A) or sometimes written as E(X | A = a), where 'a' represents a specific value of A. It represents the expected value of X when the event A has occurred.
The formula for calculating the conditional expectation is as follows:
E(X | A) = ∑(x * P(X = x | A))
Here, x represents the possible values of X, and P(X = x | A) represents the conditional probability of X taking the value x given that event A has occurred. The sum is taken over all possible values of X.
In this formula, we multiply each value of X by its corresponding conditional probability and then sum up these values to obtain the conditional expectation.
The conditional expectation provides a way to estimate the average value of X when we have additional information or when certain conditions are met. It takes into account the probability distribution of X given the occurrence of event A, rather than simply considering the marginal probabilities of the outcomes of X.
Therefore, the conditional expectation involves the use of conditional probabilities and considers the specific conditions or events under consideration.
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Related Questions
Use the table to solve. Describe the pattern for the powers of 2.
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Jacob spent 7 hours skiing and snowboarding. He skied for 3 hours 55 minutes.
How long did he spend snowboarding?
Answers
Answer:
3 hours 5 minutes
Step-by-step explanation:
Had he skied 5 minute longer, he would have skied for 4 hours, leaving 3 hours for snowboarding. Since he skied 5 minutes less than 4 hours, he snowboarded 5 minutes more than 3 hours.
You can also just subtract the times.
7 hours - 3 hours 55 minutes =
= 6 hours 60 minutes - 3 hours 55 minutes
= 3 hours 5 minutes
Answer: 3 hours 5 minutes
solve the equation -9v-9=-27 for v.
Answers
Answer:
v=2
Step-by-step explanation:
-9v-9=-27
add nine to both sides
-9v-9+9=-27+9
simplify
-9v=-18
divide both sides by -9
-9v/-9 -18/-9
simplify y=2
hope this helps :) have a nice day !!
Answer:
v=2
Step-by-step explanation:
-9v-9=-27
add nine to both sides
-9v-9+9=-27+9
simplify
-9v=-18
divide both sides by -9
-9v/-9 -18/-9
simplify y=2
3. Which of the following does not have a
value that is greater than 0?
a. (-14)
b.
y
C. 0.052
d. -42
Answers
Answer:
C. 0.052
Step-by-step explanation:
A and D are negative.
That means that they come before 0 and are therefore smaller than 0.
We do not know the value of B.
C is a positive number, meaning it comes after 0 and is therefore greater than 0.
People spend an average of 7 hours per day on their home computers with a standard deviation of 1hour. What proportion spends at least 5 hours per day on their home computers? (enter the answeras a percent rounded to the nearest hundredth as needed)
Answers
Solution;
From the given question, we have
\(\begin{gathered} \mu=7 \\ \sigma=1 \end{gathered}\)To evaluate the proportion of people that spend at least 5 hours per day on their home computers,
Step 1: Evaluate the z score value.
The z score value is expressed as
\(\begin{gathered} z=\frac{x-\mu}{\sigma} \\ where \\ x\implies sample\text{ value} \\ \mu\implies mean\text{ value} \\ \sigma\implies standard\text{ deviation} \end{gathered}\)In this case,
\(x=5\)thus, we have the z score value to be evaluated as
\(z=\frac{5-7}{1}=-2\)Step 2: Evaluate the probability that people will spend at least 5 hours per day on their home computers,
From the normal distribution table, we have
This implies that
\(P(x\ge5)=P(z\ge-2)=0.977249868052\)Hence, the proportion that spends at least 5 hours per day on their home computers is evaluated to be
\(\begin{gathered} 0.977249868052\times100 \\ =97.7249868052 \\ \approx97.72\%\text{ \lparen nearest hundredth\rparen} \end{gathered}\)
Dexter found a pair of jeans on sale for 40% off. When he brought it to the register, he discovered that all the store items were on sale for an additional 10% off. He wrote this expression to represent the final cost of the jeans based on the original price,
Answers
Answer:
i think its The sale price of the jeans is 50% of the original price.
Step-by-step explanation:
The sale price of a new sofa is $865 and sales tax is figured at 0.10 times the price. What is the total amount paid for the sofa?
Answers
Answer:
$951.50
Step-by-step explanation:
Suppose that \( \sin \theta=\frac{14}{28} \) What is the value of \( \theta \) ? Give your answer in radians and degrees. Assume that \( \theta \) is an acute angle.
Answers
The reference angle that has a sin value of 1/2 is π/6 radians or 30 degrees. Therefore, the value of θ is π/6 radians or 30 degrees.
Given that sin θ = 14/28, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 14. This yields sin θ = 1/2.
The value of sin θ equal to 1/2 corresponds to the angle θ being π/6 radians or 30 degrees in the first quadrant.
In general, the trigonometric function sin θ represents the ratio of the length of the side opposite the angle θ to the length of the hypotenuse in a right triangle. For sin θ to be positive, the angle θ must lie in the first or second quadrant. Since we are assuming θ to be an acute angle, it falls within the first quadrant.
In the first quadrant, the reference angle that has a sin value of 1/2 is π/6 radians or 30 degrees. Therefore, the value of θ is π/6 radians or 30 degrees.
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What is the measure of the missing angle DBA
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it’s a supplementary angle so it equals 180 degrees and 180-121= 59
Find the 13th geometric sequence 1, 2, 4, …
Answers
Answer:
24.
Step-by-step explanation:
The pattern is clearly going up by twos.
So continuing the pattern,
1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
1 2 3 4 5 6 7 8 9 10 11 12 13
the average of 8 girls is 15 and the average of 6 girls is 13 find the average of the other two girls with equal age
Answers
Answer:
21
Step-by-step explanation:
Since the girls have the same age, let their age be x.
Then, their average is
\(\frac{x+x}{2} = \frac{2x}{2} = x\)
Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)
Also, we have,
\(\frac{S_{8}}{8} =15 - eq(2)\)
\(\frac{S_{6}}{6} =13 - eq(3)\)
Then eq(2):
(from eq(1) and eq(3))
\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)
The average of the other two girls with equal age is 21
A Galaw $20 is 800 Dn cheaper than the $21. Which of the below exprestions models tis shabon if 520 represerts ?we price of the 320 and 521 represerts the grice of the sa1? a) S21=S20−800 b) S20=S21+800 c) S20=800 d) S21S20=S21−800
Answers
The expression that models the relationship between the prices is option a) S21=S20−800.
According to the given information, a Galaw $20 is $800 cheaper than the $21. Let's denote the price of the Galaw $20 as S20 and the price of the $21 as S21.
Since the Galaw $20 is $800 cheaper than the $21, we can represent this relationship with the equation S21 = S20 - 800.
This equation states that the price of the $21 is equal to the price of the Galaw $20 minus $800. Therefore, option a) S21 = S20 - 800 is the correct expression that models the given scenario.
The other options do not accurately represent the relationship between the prices. Option b) S20 = S21 + 800 suggests that the Galaw $20 is $800 more expensive than the $21, which contradicts the given information. Option c) S20 = 800 implies that the price of the Galaw $20 is a fixed value of $800, regardless of the price of the $21. Option d) S21S20 = S21 - 800 does not accurately represent the relationship between the prices.
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Clarence sells yearly subscriptions to a particular magazine. he sells at least 10 and no more than 25 subscriptions each week. the function represents the amount of money earned for selling t subscriptions each week. what is the practical range of the function?
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The practical range of the function is between $100 and $625.
This can be calculated using the formula y=10x, where x is the number of subscriptions sold each week and y is the amount of money earned. To calculate the amount of money earned for selling t subscriptions each week, we can use the formula y = 10t. This can be interpreted as saying the amount of money (y) is equal to 10 times the number of subscriptions sold (t). For example, if Clarence sells 15 subscriptions each week, then we can calculate the amount of money he earns by plugging in t = 15. y = 10(15) = 150. This means Clarence earns $150 each week by selling 15 subscriptions. For example, if Clarence sells 10 subscriptions each week, he would earn $100 (10 x 10 = 100). If he sells 25 subscriptions each week, he would earn $625 (25 x 25 = 625). The practical range of the function is therefore $100 to $625.
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State three functions F1, F2, F3 whose derivatives are f(x) = 3x?. Now sketch all three of your functions on the same coordinate plane. Compare these with f(x) = 3x?
Answers
Three functions F1, F2, F3 whose derivatives are f(x) = 3x are:
1. F1(x) = (3/2)x^2 + C1
2. F2(x) = (3/2)x^2 + C2
3. F3(x) = (3/2)x^2 + C3
Here, C1, C2, and C3 are constants.
To sketch all three functions on the same coordinate plane, follow these steps:
Step 1: Draw the x and y axes on the coordinate plane.
Step 2: Plot the parabola y = (3/2)x^2 for the basic shape of all three functions.
Step 3: For each function, add the constant C1, C2, or C3 to the parabola to vertically shift it up or down.
Step 4: Label each function F1, F2, and F3 on the graph.
When comparing these functions with f(x) = 3x, we can see that F1, F2, and F3 are all parabolic functions, while f(x) = 3x is a linear function. The functions F1, F2, and F3 represent the antiderivatives (indefinite integrals) of f(x) = 3x, and their shapes are influenced by the constants C1, C2, and C3.
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Assume double[][] x = new double[4][5], what are x.length and x[2].length? a. 4 and 4
b. 4 and 5 c. 5 and 4 d. 5 and 5
Answers
The x.length is the number of rows, which is 4. x[2].length is the number of columns in the 3rd row, which is 5. The expression "new double[4][5]" creates a 2D array of doubles with 4 rows and 5 columns. The correct answer is (b) 4 and 5.
The expression double[][] x = new double[4][5] creates a 2D array x with 4 rows and 5 columns. Therefore, x.length gives the number of rows, which is 4. And x[2].length gives the number of columns in the 3rd row (since array indices start at 0), which is 5. Therefore, the correct option is (b) 4 and 5.
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How will you describe the graph of exponential function?
Answers
The graph of exponential function, is described below.
What is an exponential function?
The mathematical formula f(x) = e^x stands for the exponential function. The term, unless specifically stated otherwise, generally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
The formula for an exponential growth function is y = ab^x, where a > 0 and b > 1. As can be seen in the example of f(x) = 2x below, the graph will ascend. The numbers get smaller as x gets closer to negative infinity, as you can see.
If b > 1 , then the graph's slope is positive and exponential growth is depicted. The value of y approaches infinity as x rises. The value of y approaches zero as x falls.
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If X - 14 = 465, what is the value of X?
Answers
Answer: The value of x is 479
Step-by-step explanation:
x -14 = 465
+14 +14
x= 479
Answer:
x=479
Step-by-step explanation:
x-14=465 Move constant to the right-hand side and change its sign
x=465+14 add the numbers
x=479
HOPE THIS HELPS :)
what is the probability that the first son of a woman whose mother's brother has lesch-nyhan syndrome will be affected?
Answers
If a woman's uncle has Lesch-Nyhan syndrome and her father carries the mutation, the probability of her first son being affected is 50%.
Lesch-Nyhan syndrome is an X-linked recessive genetic disorder, which means it is caused by a mutation on the X chromosome and is passed down through families primarily from affected fathers to their daughters. The probability that a son of a woman with an affected uncle (mother's brother) will be affected depends on the genetic status of the woman's father and the mother's X chromosome that she inherited from her mother.
If the woman's father does not carry the mutation, she will not carry the mutation herself and cannot pass it on to her children. In this case, the probability of her first son being affected is 0%.
If the woman's father carries the mutation, she has a 50% chance of inheriting the mutated X chromosome from her father and a 50% chance of inheriting a normal X chromosome from her mother. In this case, if the woman is a carrier of the mutation, her first son has a 50% chance of inheriting the mutation from her and being affected.
It's important to note that this is a simplified answer and that more complex genetic testing and counseling may be necessary to determine the specific risk in a particular family.
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find the chi-square value corresponding to a sample size of 17 and a confidence level of 98 percent.
Answers
the chi-square value corresponding to a sample size of 17 and a confidence level of 98 percent is 31.410.
To find the chi-square value corresponding to a sample size of 17 and a confidence level of 98 percent, we need to look up the critical value of the chi-square distribution.
The chi-square distribution is determined by the degrees of freedom, which in this case is equal to the sample size minus 1. Since the sample size is 17, the degrees of freedom will be 17 - 1 = 16.
To find the chi-square value at a 98 percent confidence level, we need to determine the critical value associated with an alpha level of 0.02 (since the confidence level is 98 percent, the remaining 2 percent is split into two tails, each with a probability of 1 percent or 0.01).
Using a chi-square distribution table or a statistical calculator, the critical chi-square value with 16 degrees of freedom and an alpha level of 0.02 is approximately 31.410.
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If it takes five elves, five minutes to make five dolls, then how long will it take 100 elves to make 100 dolls?.
Answers
If it takes five elves, five minutes to make five dolls, then 5 minutes will it take 100 elves to make 100 dolls.
In the given question,
If it takes five elves, five minutes to make five dolls, then we have to find how long will it take 100 elves to make 100 dolls.
5 elves make 5 dolls = 5 minutes
1 elves make 5 dolls in = 5×5 minutes
1 elves make 5 dolls in = 25 minutes
So 1 elves make 1 dolls in = 25/5 minutes
1 elves make 5 dolls in = 5 minutes
So 1 elves make 100 dolls in = 5×100 minutes
1 elves make 5 dolls in = 500 minutes
So 100 elves make 100 dolls in = 500/100 minutes
100 elves make 100 dolls in = 5 minutes
Hence, if it takes five elves, five minutes to make five dolls, then 5 minutes will it take 100 elves to make 100 dolls.
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Becky and Julia decided to go on vacation. They found a great deal for 20% off any cruise. If their budget is $1,115, where can they go on their vacation? Mexico- $1,499, Caribbean- $1,250, Jamaca- $1,375, Florida- $1,150. Standard 10% sales tax applies
Answers
Answer:
Step-by-step explanation:
20% of 1150 is 230, so 1150-230=920
if the tax is applied after the discount, you find 10% of 920 (which is 92)
you add that to the discounted price 920+92= 1012, so they could go to florida.
Find the value of z that corresponds to the following: a) Area = 0.1210 b) Area = 0.9898 c) 45th percentile
Answers
a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.
b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.
c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.
a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.
b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.
c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.
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v − 15 = −27. Help ty
Answers
Answer:
\(\boxed {v = -12}\)
Step-by-step explanation:
Solve for the value of \(v\):
\(v - 15 = -27\)
-Add both sides by \(15\):
\(v - 15 + 15 = -27 + 15\)
\(\boxed {v = -12}\)
Therefore, the value of \(v\) is \(-12\).
A plane is traveling at 600 miles per hour. How many feet per second is it traveling?
Answers
Answer:
600
Step-by-step explanation:
Answer:
880 ft/sec
Step-by-step explanation:
the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. find the probability that a randomly selected passenger has a waiting time minutes.
Answers
According to the uniform distribution, there is a 0.625 = 62.5% chance that a randomly chosen passenger will have to wait longer than 2.25 minutes.
The boundaries of a uniform distribution are a and b.
The likelihood of discovering a value greater than x is:
P(X > x)=b-x/b-a
In this issue, the distribution of time is evenly spaced between 0 and 6 minutes, therefore
a=0 b=6
P(X > x)= 6-2.25/6-0
=0.625
0.625 = 62.5% probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
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Jerry grows two different types of oranges. He wants to know which type of oranges weighs more. he takes a random sample of oranges from each type of tree and creates the dotshown with their weights, and ounces. Based on these data., Which statement is true?
Answers
The answer is B (There is evidence that a Type BBB orange typically weighs more than a Type AAA orange.) this is right on edulastic
10) Determine whether the events of rolling a fair die two times are disjoint, independent, both, or neither. A) Disjoint. B) Exclusive. C) Independent. D) All of these. E) None of these.
Answers
The answer is option (C), that is, the events of rolling a fair die two times are independent. The events are neither disjoint nor exclusive.
When rolling a fair die two times, one can get any one of the 36 possible outcomes equally likely. Let A be the event of obtaining an even number on the first roll and let B be the event of getting a number greater than 3 on the second roll. Let’s see how the outcomes of A and B are related:
There are three even numbers on the die, i.e. A={2, 4, 6}. There are four numbers greater than 3 on the die, i.e. B={4, 5, 6}. So the intersection of A and B is the set {4, 6}, which is not empty. Thus, the events A and B are not disjoint. So option (A) is incorrect.
There is only one outcome that belongs to both A and B, i.e. the outcome of 6. Since there are 36 equally likely outcomes, the probability of the outcome 6 is 1/36. Now, if we know that the outcome of the first roll is an even number, does it affect the probability of getting a number greater than 3 on the second roll? Clearly not, since A∩B = {4, 6} and P(B|A) = P(A∩B)/P(A) = (2/36)/(18/36) = 1/9 = P(B). So the events A and B are independent. Thus, option (C) is correct. Neither option (A) nor option (C) can be correct, so we can eliminate options (D) and (E).
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The shadow of a flagpole is 37 meters long. The angle of elevation from the end of the shadow to the top of the flagpole is 15°. What is the height of the flagpole? Round to the nearest meter.
Answers
Answer:
if you make a drawing, you will see that you have created a right triangle with the angle of elevation opposite the leg that is the height of the flagpole.
The length of the shadow is the other leg, adjacent to the angle of elevation.
Applying the trigonometric identity for right triangles:
tan(angle of elevation) = opposite/adjacent -->
tan(15) = height/37 -->
height = 37 * tan(15) = 9.9
Pythagorean Theorem
(Rounding)
Find the length of the third side. If necessary, round to the nearest tenth.
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER AND POINTS!!!!
IMAGE DOWN BELOW!!
Answers
Work Shown:
\(a^2 + b^2 = c^2\\\\a^2 + 5^2 = 8^2\\\\a^2 + 25 = 64\\\\a^2 = 64-25\\\\a^2 = 39\\\\a = \sqrt{39}\\\\a \approx 6.244998\\\\a \approx 6.2\)
the simple process of counting the number of observations (cases) that are classified into certain categories is known as .
Answers
The process of counting the number of observations is knowns as Tabulation.
What is tabulation?The logical representation of the numerical data written in rows and columns is known as tabulation. It helps in to facilitate the statistical analysis. The data that can be organized in the form of table is termed as tabulation. The data in the table can be represented in a systematic manner. The main objective of tabulation is to present the systematic data in a brief manner.
There are two types of tabulation. They are:
1.Simple tabulation
2.Complex tabulation
A simple example for the tabulation is, The population of the people is divided into religion, caste, gender, age etc.
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