Question

Let W be a normally distributed random variable with mean 25 and variance 4.

(a) What type of distribution does Y = [(W−25)/2]^2 have? Name: ____ Parameter(s): ____

(b) Let W1, W2, . . . , W100 be a random sample from a normal population with mean 25 and variance 4.

i. What type of distribution does W(bar) have? Name:____ Parameter(s):____

ii. What type of distribution does (99S^2)/4 have? Name:___ Parameter(s)____

Answer 1

From the given information,

The required correct answers are,

a. Name:- Chi-square

Parameter:- Degrees of freedom (n)=1

b. i)

Name:- Normal

Parameters:- Mean=25 and variance=0.04

ii)

Name:- Chi-square

Parameter:- Degrees of freedom (n)=99

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