x is a random variable that has a distribution function f. if a,b ∈r, and a > 0, what is the distribution function of y = ax b?

Answers

Answer 1

Given a random variable X with a probability distribution function f(x), and constants a and b with a > 0, we want to find the distribution function of

\(Y = aX + b.\)

To find the distribution function of Y, we need to consider the transformation of the original function f(x). Since Y is defined as a linear transformation of X, we can apply the change of variables method to determine the distribution function of Y.

First, let's express X in terms of

\(Y: X = (Y - b) / a.\)

Next, we need to find the Jacobian of the transformation, which in this case is simply the derivative of X with respect to Y:

\(dX/dY = d((Y - b) / a)/dY = 1/a.\)

Now, we can find the probability distribution function of Y, denoted as g(y), using the original distribution function f(x) and the Jacobian:

\(g(y) = f(x) * |dX/dY| = f((Y - b) / a) * (1/a).\)

In conclusion, the distribution function of Y = aX + b is given by

\(g(y) = f((Y - b) / a) * (1/a),\)

where f(x) is the distribution function of the random variable X, and a and b are constants with a > 0.

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Related Questions

Keegan had 3.25 pounds of flour. After making bread, he had 1.75 pounds of flour left over. i know its 1.5 but whats the Equation?

Answers

Answer:

3.25 - 1.75 = 1.50 pounds of flour

Step-by-step explanation:

Which statement can you use to conclude that quadrilateral xyzw is a parallelogram

Which statement can you use to conclude that quadrilateral xyzw is a parallelogram

Answers

Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.

it is estimated that 70% of ucf students participate in anti-racist practices. in a sample of 50 ucf students, how many would you expect to participate in anti-racist practices?

Answers

35 expect to participate in anti-racist practices.

anti-racist practices=Anti-racism encompasses a range of ideas and political actions which are meant to counter racial prejudice, systemic racism, and the oppression of specific racial groups. Anti-racism is usually structured around conscious efforts and deliberate actions which are intended to provide equal opportunities for all people on both an individual and a systemic level. As a philosophy, it can be engaged in by the acknowledgment of personal privileges, confronting acts as well as systems of racial discrimination, and/or working to change personal racial biases. Major contemporary anti-racism efforts include Black Lives Matter organizing and workplace antiracism.

Expect value= n*p=0.70*50

=35

Answer=35

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Convert the following equation
into standard form.
y = -x - 3

Convert the following equationinto standard form.y = -x - 3

Answers

Answer:

x+y=−3

Step-by-step explanation:

hope this heps:)

Answer:

x+y=-3 (put -3 into the box)

Step-by-step explanation:

add x to both sides, and you get x+y= -3.

show work please and no links

show work please and no links
show work please and no links
show work please and no links
show work please and no links

Answers

Answer:

man it’s one in the morning and your picture is blurry a f

Step-by-step explanation:

Your pictures are blurry and one of them is upside down

What percentage of the measurements in the data set lie to the right of the median? ___ % What percentage of the measurements in the data set lie to the left of the upper quartile? ___ %

Answers

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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I NEED HELP PLS WITH THIS MATH QUESTION ASAP The Coat on Sale
Harris's Department Store was
trying to sell a winter coat which
n o one seemed to want. First, they
tried to sell it for 20% off the
marked price, but no one would
buy it. Then, they tried to sell it for
25% off the first sale price, but still
no one would buy it. Finally, they
offered it for 30% off of the second
sale price, and someone actually
bought the coat for $21.
What price did Harris's originally
try to sell the coat for?

Answers

Answer:

$50

Step-by-step explanation:

To get previous prices, divide by what you would have multiplied to get the next price. X*.70 (that’s 30% off)=21. So... 21/.70=X. Repeat for each price change... (((21/.7)/.75)/.8)=$50.

Answer:

$50 is the answer

A restaurant offers delivery for their pizzas. The total cost is a delivery fee added to the price of the pizzas. One customer pays $25 to have 2 pizzas delivered. Another customer pays $58 for 5 pizzas. What is the cost of one pizza?

Answers

Answer:

$11

Step-by-step explanation:

11 x 2 = 22

25 - 22 = 3

11 x 5 = 55

58 - 55 = 3

Delivery Fee is $3

Every Pizza is $11

Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 30 more adult tickets than student tickets to the fall play. If the class collected 840 from ticket sales, how many adult tickets were sold?

Answers

The number of adult tickets that were sold would be = 435 tickets.

What is a ticket?

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

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a pole that is 2.8 mm tall casts a shadow that is 1.37 m long. At the same time, a nearby building casts a shadow that is 36.25 m long. how tall is the building? round your answer to the nearest meter.

Answers

Answer:

this is the correct answer

a pole that is 2.8 mm tall casts a shadow that is 1.37 m long. At the same time, a nearby building casts
Answer is 74 meters

plsss answer i'll give 50

plsss answer i'll give 50

Answers

Step-by-step explanation:

I know it not all but this is what I have

plsss answer i'll give 50


Write an equation in slopeintercept form that describes the line containing the points (-1,0) and (2,4) .

Answers

The equation in slope-intercept form y = 4/3 x + 4/3 contains the points (-1 , 0) and (2 , 4).

An equation of a line in slope-intercept form is given by the formula y = mx+ b, where m is the slope of the line and b is the y- intercept.

If you know two points on a line, you can use them to write the equation of the line in slope-intercept form.

First is to find the slope of the line using the two given points.

let Point 1(-1 , 0) and Point 2(2 , 4)

slope = m = (y2 - y1) / (x2 -x1)

m = (4 - 0) / (2 - -1)

m = 4/3

Next, use the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.

y = mx+ b

y = 4/3 x + b

Using Point 1,

0 = 4/3 (-1) + b

0 = -4/3 + b

b = 4/3

Finally, set up the equation of the line in slope-intercept form.

y = mx+ b

where m = 4/3 and b = 4/3

y = 4/3 x + 4/3

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Carlton has a job offer for a position as a telemarketer. The job pays $60 per week, plus a
$15 commission for each sale he makes. How many sales would Carlton have to make in
a week in order to earn $240?

Answers

Answer:

He would have to make 12 sales a week in order to make $240

Step-by-step explanation:

So every week the job pays him $60

And $15 more every sell he makes So 15x12=180

So if he  makes 12 sells in a week he will make $180 dollars.

Plus the 60 the job pays him every week

So 180+60=$240

PLS HELP!!
A ball is thrown straight up from the top of a building that is 400 ft high with an initial velocity of 64 ft/s. The height of the object can be modeled by the equation s(t) = -16t2 + 64t + 400.

In two or more complete sentences explain how to determine the time(s) the ball is higher than the building in interval notation.

Answers

From the graph of the function, the ball is higher than the building (400 feet) between the interval (0, 4)

What is an equation?

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let h represent the height of the ball after spending t seconds. A ball is thrown straight up from the top of a building that is 400 ft high with an initial velocity of 64 ft/s.

Given the equation:

h(t) = -16t² + 64t + 400

From the graph of the function, the ball is higher than the building (400 feet) between the interval (0, 4)

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PLS HELP!!A ball is thrown straight up from the top of a building that is 400 ft high with an initial

use the following information for question 2 - 6: tv advertising agencies face increasing challenges in reaching audience members because viewing tv programs via digital streaming is gaining in popularity. the harris poll reported on november 13, 2012, that 53% of 2343 american adults surveyed said they have watched digitally streamed tv programming on some type of device. question 2: what is the sample proportion?

Answers

The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

Given that,

Because watching TV via digital streaming is becoming more and more common, tv advertising companies are having a harder time connecting with viewers. 53% of the 2343 American adults surveyed by the Harris Poll on November 13, 2012, claimed they had viewed digitally streamed television content on at least one device.

We have to find what is the sample proportion? firstly, the z-critical value is ? What is the confidence interval at 99%?

We know that,

n = 2343

Point estimate = sample proportion = \(\hat p\) = 0.530

1 - \(\hat p\) = 1 -0.530 = 0.470

At 99% confidence level

α = 1-0.99% =1-0.99 =0.01

α /2 =0.01/ 2= 0.005

Z(α /2) = Z0.005 = 2.576

Z (α/2) = 2.576 = 2.58

Margin of error = E = Z (α/2) × √((\(\hat p\) × (1 - \(\hat p\) )) / n)

=2.576 × (√(0.530×(0.470) /2343 )

= 0.027

A 99% confidence interval for population proportion p is ,

\(\hat p\)- E < p < \(\hat p\) + E

0.530 -0.027 < p < 0.530 +0.027

0.503 < p < 0.556

( 0.503, 0.556 )

Therefore, The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

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does the data give evidence of an association between scoring at least 21 points and the football team winning the game? there is a strong, negative association. there is a strong, positive association. there is a weak, negative association. there is a weak, positive association.

Answers

Considering the relative frequencies in this problem, the association between scoring 21 points and winning the game is as follows:

There is a strong, positive association.

What is a relative frequency?

The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

From the table given at the end of the answer, we have that when the team scored at least 21 points, an interval composed of 28 games, the team won 25 games and lost only 3, hence the relative frequency of wins when the team scores at least 21 points is of:

25/28 = 0.8929 = 89.29%.

Due to this high frequency of wins, there is a strong and positive association between scoring 21 points and winning the game

What is the missing information?

The table with the team's results is given by the image at the end of the answer.

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does the data give evidence of an association between scoring at least 21 points and the football team

Find the surface area of the cylinder in terms of π
A) 32π m^2
B) 64π m^2
C) 80π m^2
D)96π m^2

Answers

The surface area of a cylinder can be calculated using the formula S = 2πrh + 2πr2, where r is the radius of the cylinder, and h is its height. the surface area of the cylinder is 96π m2, making the answer D) 96π m2.

In this case, the radius is 8m and the height is 4m. Plugging these values into the formula yields S = 2π(8)(4) + 2π(82), which simplifies to S = 64π + 64π, or S = 96π m2. Therefore, the answer is D) 96π m2.

The surface area of a cylinder is the total area of the two circular ends and the curved sides. To calculate the surface area, we need to know the radius, r, of the cylinder and its height, h. The formula to find the surface area of a cylinder is S = 2πrh + 2πr2. In this problem, the radius is 8m and the height is 4m. Plugging these values into the formula, we get S = 2π(8)(4) + 2π(82). Simplifying this expression, we get S = 64π + 64π, which can be further simplified to S = 96π m2. Therefore, the surface area of the cylinder is 96π m2, making the answer D) 96π m2.

S = 2π(8)(4) + 2π(82)

 = 64π + 64π

 = 96π m2

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how do i solve i dont under stand​

how do i solve i dont under stand

Answers

hope this helps

lmk if you need more explanation
how do i solve i dont under stand

Will the probability of winning plus the probability of losing always equal 1?​

Answers

Answer:

\( \sf \huge \fbox{{No}}\)

Step-by-step explanation:

Consider an event or an competition is going on. two competetors (let A & B) are racing with each other to win something. Let's see what are the possible events that can occur,

Event 1- Competetor A wins the race against B

Event 2- Competetor B wins the race against B

Event 3- Match draw, either both of them are winner or none of them are winner.

So there are three possible events that can occur & we know that total probability always equals one, let's calculate the probability for each event individually.

The probability of occuring each event is equal, hence,

\( \sf Probability \: of \: winning \: p(w)= \frac{1}{3} \)

\( \sf Probability \: of \: losing \: p(l)= \frac{1}{3}\)

\( \sf Probability \: of \: match \: draw \: p(d)= \frac{1}{3}\)

Now,

the sum of probability of winning & probability of losing,

\(p(w) +p(l) = \frac{1}{3} + \frac{1}{3} = \frac{2}{3} ≠1\)

Hence, the result is contradiction to the statement the probability of winning plus the probability of losing always equal 1.

\(\sf \small \pink{Thanks }\: \green{for} \: \blue{joining} \: \orange{brainly } \: \red{community}!\)

Put the following in slope-intercept form.
4x-2y6

Answers

Answer: 2( - y^6 + 2x)

Step-by-step explanation: Coz I juss know

PLS TELL ME WHICH ONE IS TRUE PLS DONT LIE

PLS TELL ME WHICH ONE IS TRUE PLS DONT LIE

Answers

I believe the answer is B sorry if i am incorrect
a is the correct answer

A line has a y-intercept at (0, 4) and an x- intercept at (6, 0). What is the slope of the line?

Answers

Answer:

\(m=\frac{-2}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Step-by-step explanation:

Step 1: Define

y-int (0, 4)

x-int (6, 0)

Step 2: Find slope m

Substitute:                    \(m=\frac{0-4}{6-0}\)Subtract:                       \(m=\frac{-4}{6}\)Simplify:                        \(m=\frac{-2}{3}\)

The mass of a radioactive substance follows a continuous exponential decay model with a decay rate parameter of 7% per day. A sample of this radioactive substance was taken two days ago. If the sample has a mass of 3 kg today, find the initial mass of the sample. Round your answer to two decimal places.

Answers

The initial mass of the sample is approximately 3.45 kg.

To find the initial mass of the radioactive sample, we can use the exponential decay model. The general form of the exponential decay model is given by:

M(t) = M0 * \(e^{(-kt)}\)

Where:

M(t) is the mass at time t,

M0 is the initial mass,

k is the decay rate parameter,

e is the base of the natural logarithm (approximately 2.71828).

In this case, we are given that the decay rate parameter is 7% per day, which can be written as k = 0.07. We also know that the mass of the sample today is 3 kg, and it was taken two days ago. Therefore, t = 2.

Using the given values in the exponential decay model equation, we can solve for the initial mass M0:

3 = M0 * \(e^{(-0.07 * 2)}\)

Simplifying the equation:

3 = M0 * \(e^{(-0.14)}\)

Dividing both sides by \(e^{(-0.14)}\):

\(M0 = 3 / e^{(-0.14)}\)

Using a calculator, we can evaluate the right-hand side of the equation:

M0 ≈ 3 / 0.868745

M0 ≈ 3.45

Therefore, the initial mass of the sample is approximately 3.45 kg.

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What is the value of x?

What is the value of x?

Answers

Answer:

-1

Step-by-step explanation:

to be honest im not sure if its right or not but if u look at the question there are 5 x making it -5 and 6 1's

Part C. Select all the amounts of time, in minutes, that Vanessa could leave the hose running.
0 7 minutes
07.5 minutes
9 minutes
9.75 minutes
0 10.3 minutes
0 12 minutes

Answers

Answer:

The hose can run for 7.5 minutes, 9 minutes, and 12 minutes.

The hose can't run for 0 minutes, 7 minutes, 9.75 minutes, or 10.3 minutes.

Here's why:

Vanessa needs to water her plants for at least 7.5 minutes.

Vanessa can't leave the hose running for more than 12 minutes because it will waste water.

Step-by-step explanation:

Answer:

The hose can run for 7.5 minutes, 9 minutes, and 12 minutes.

The hose can't run for 0 minutes, 7 minutes, 9.75 minutes, or 10.3 minutes.

Here's why:

Vanessa needs to water her plants for at least 7.5 minutes.

Vanessa can't leave the hose running for more than 12 minutes because it will waste water.

Step-by-step explanation:

What is 7n - 2 - 9n + 5? Pls help

Answers

answer here:

-2n+3

....

Answer:

7n-9n-2+5

-2n+3 or 3-2n

Step-by-step explanation:

Chris ate 1/8 of a banana cream pie with a 14 inch diameter. What is the area of the remaining portion of the pie? Round to the nearest tenth. Use 3.14 for pi.

Answers

Answer:

Area of a circle is pi x radius squared.

If we use 3.14 for pi, and the Diameter is 14 so that radius will be 7 (half of diameter), this means we have 3.14 x 7 squared = 153.86.

Total area of pie is 153.86.

If 1/8 was eaten that means 7/8 are left.

153.86/8= 19.23

19.23 x 7 = 134.6 to the nearest tenth..

Write a positive or negative integer that represents the situation.
You withdraw $42 from an account.
The integer
represents the situation.
8

Hi can someone help me I just started 6 grade I need help

Answers

Answer:

-42

Step-by-step explanation:

If you withdraw an amount, it means that you are taking it out. On the other hand, if you were to deposit an amount, you are putting money in. Taking something out means that you have less of it, so -42 would be the answer. If you were to deposit an amount, the answer would be +42 since you are adding it in.

In a recent storm, an 18-foot utility pole broke and fell leaving a 5-foot tall portion upright. How far is the top of the pole from the base of the pole?

Answers

Answer: \(12\ ft\)

Step-by-step explanation:

Given

Total height of utility pole is 18 ft

After breakage, only 5 foot tall portion is standing

The fallen part is \(18-5=13\ ft\) in length

From the figure, apply the Pythagoras theorem

\(\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft\)

Thus, the fallen part is \(12\ ft\) away from the base of the pole.

In a recent storm, an 18-foot utility pole broke and fell leaving a 5-foot tall portion upright. How

choose the best graph to match the given expression.
F(x)= [x+1]

Answers

Answer:

Step-by-step explanation:

I don't see a graph from which to choose.  Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?

The graph of functions

(F(x) = (x+1), and

(F(x) = |x+1| are both attached.

choose the best graph to match the given expression. F(x)= [x+1]
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Market structures vary due to: Multiple select question. demand conditions the number of firms in the market scarcity technology and costs ease with which firms can enter or exit the industry the relative size of firms Rough Industries reported a deferred tax liability of $9.00 million for the year ended December 31, 2021, related to a temporary difference of $36 million. The tax rate was 25%. The temporary difference is expected to reverse in 2023 at which time the deferred tax liability will become payable. There are no other temporary differences in 2021-2023. Assume a new tax law is enacted in 2022 that causes the tax rate to change from 25% to 15% beginning in 2023. (The rate remains 25% for 2022 taxes.) Taxable income in 2022 is $48 million. Income tax expense in 2022 for Rough would be:A $9.6 millionB $12.4 millionC $8.4 millionD $15.6 millio Ice Choose one: A. is denser than water. B. has a low albedo, which explains why it floats. 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