Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the...

Question

Question

Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X. Variance of Z, i.e., σ2 is:

math Statistics-And-Probability

Answer 1

Answer #1

Solution:

For random variable X, we are given

Mean = E(X) = 3

Variance = Var(X) = 2

Z = 1 + 5X

We have to find variance of Z.

We know the rule for change of origin and scale for variance of linear combination of random variable given as below:

If Z = a + bX, then Var(Z) = b²*Var(X)

(Change of origin is invariant for variance.)

Variance of Z = σ² = Var(Z) = 5^2*Var(X) = 25*2 = 50

Answer: 50

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Answer 2

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