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

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​

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  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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