Find the distribution of W = X2 when
(a) X is N(0, 4),
(b) X is N(0, σ2).
Step 1 of 3 :
A random variable X is normally distributed with mean and standard deviation .
The probability density function is
The claim is to find the distribution of w = when.
X ~ N(0, 4)X ~ N(0,
In general, ~ with one degrees of freedom.
Where, v =
The probability density function of v is
P( V v) = dy , 0 < v <
Step 2 of 3 :
Here, X follows N(0,4)
w = , v = it follows with one degrees of freedom.
Let w =
Then, P(W w) = P(4v w)
= P(v )
= dy - (1)
Let, z = 4y
Substitute in equation 1
Which follows gamma distribution with = ½ and = 8
P(W w) = be the distribution function of w = when
X ~ N(0, 4).
Textbook: Probability and Statistical Inference
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
The answer to “Find the distribution of W = X2 when(a) X is N(0, 4),(b) X is N(0, ?2).” is broken down into a number of easy to follow steps, and 16 words. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Since the solution to 9E from 3.3 chapter was answered, more than 301 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 9E from chapter: 3.3 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. This full solution covers the following key subjects: distribution, Find. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271.