Question

The area under the normal curveis
If X is normal with mean 3 and variance 1. then X-3 is a variate with mean 0 and variance 1​

Answer 1

SOLUTION

TO DETERMINE

1. The area under the normal curve

2. To prove : If X is normal with mean 3 and variance 1. then X-3 is a variate with mean 0 and variance 1

EVALUATION

1. The area under the normal Curve is 1

2. Here it is given that X is normal with mean 3 and variance 1

So E(X) = 3 & Var(X) = 1

Now

E(X - 3)

= E(X) - E(3)

= 3 - 3

= 0

X - 3 is a variate with mean 0

Again

Var(X-3)

= 1² Var(X)

= 1 × 1

= 1

X - 3 is a variate with variance 1

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