Let X ∼ N\(\left(\mu, \sigma^{2}\right)\), and let Z = \((X-\mu) / \sigma\) . Use Equation (4.25) to show that Z ∼ N(0, 1).
Equation transcription:
Text transcription:
(\mu, sigma^{2})
(X-\mu) / sigma
Answer:
Step 1 of 1:
In this question, we are asked to prove , using equation
.
Let , and let
Equation state that,
Let , and let
and
be constants. Then,
………..(1)
We know that,
………(2)
From equation (2), let,
Now we can substitute value of and
,
Substitute the value of ,
,
and
into equation (1),
Hence proved.