Question

Let Z be a standard normal random variable and let Y = Z2. Use transformation of...

Let Z be a standard normal random variable and let Y = Z2. Use transformation of variables to find the distribution of Z, which distribution is it?

Include the domain as part of your answer.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

PDF of standard normal variable Z is

CDF of standard normal variable Z is


And for standard normal variable

Since range of Z is to so range of Y is 0 to . The CDF of Y will be

  

So CDF of Y is

Differentiating above gives the PDF of Y so

So pdf of Y is

It is PDF of Chi-square distribution .

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round...
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ? ?0.25) Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ? 1.24) Let z be a random variable with a standard normal distribution. Find the indicated probability. (Enter your answer to four decimal places.) P(?2.20 ? z ? 1.08)
A: Let z be a random variable with a standard normal distribution. Find the indicated probability....
A: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ≤ 1.11) = B: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ≥ −1.24) = C: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−1.78 ≤ z...
Let X and Y be independent, standard normal variables, S = max{X, Y }, Z standard...
Let X and Y be independent, standard normal variables, S = max{X, Y }, Z standard normal. Prove that S2 and Z2 have the same distribution.
Let X be a normal random variable with ?=−10 and ?=2. Let Z be a standard...
Let X be a normal random variable with ?=−10 and ?=2. Let Z be a standard normal random variable. Draw density plots for both random variables on the same graph. You will want an x-axis that goes from around -20 to around 5. Your y-axis will start at zero and will need go high enough to cover the highest density. Recall that the density of a normal random variable at the point ? with mean ? and standard deviation ?...
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round...
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−0.53 ≤ z ≤ 2.04) =
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round...
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−2.10 ≤ z ≤ −0.46)
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Enter...
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) P(z ≥ 1.41) = Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Enter a number. Round your answer to four decimal places.) The area between z = 0.41 and z = 1.82 is .
2. Let the random variable Z follow a standard normal distribution, and let z1 be a...
2. Let the random variable Z follow a standard normal distribution, and let z1 be a possible value of Z that is representing the 10th percentile of the standard normal distribution. Find the value of z1. Show your calculation. A. 1.28 B. -1.28 C. 0.255 D. -0.255 3. Given that X is a normally distributed random variable with a mean of 52 and a standard deviation of 2, the probability that X is between 48 and 56 is: Show your...
Let Z be a standard normal random variable. Use the calculator provided, or this table, to...
Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of . P (1.18 _< Z _< c) = 0.0854 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Let Z be a standard normal random variable. Use the calculator provided, or this table, to...
Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c.=P( -0.9 ≤ Z ≤ c)=0.8037 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT