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.