Question

Let Z be a standard normal random variable and let Y =
Z^{2}. Use transformation of variables to find the
distribution of Z, which distribution is it?

Include the domain as part of your answer.

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 .

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. (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 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 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 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 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 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 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 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 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

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 23 minutes ago

asked 24 minutes ago

asked 32 minutes ago

asked 38 minutes ago

asked 42 minutes ago

asked 49 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago