If variance of x is 5, then find the variance of (2 – 3x)(a) 10(b) 45(c) 5(d) -13

Question

If variance of x is 5, then find the variance of `(2 – 3x)`

(a) 10
(b) 45
(c) 5
(d) -13

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Solution

The variance of a random variable X is given by Var(X). If we have a new variable Y = aX + b, where a and b are constants, then the variance of Y is given by Var(Y) = a^2 * Var(X).

In this case, X has a variance of 5, and we want to find the variance of Y = 2 - 3X.

Step 1: Identify the constants a and b in the equation Y = aX + b. Here, a = -3 (the coefficient of X) and b = 2 (the constant term).

Step 2: Substitute the values of a and Var(X) into the formula Var(Y) = a^2 * Var(X).

Var(Y) = (-3)^2 * 5 = 9 * 5 = 45.

So, the variance of Y = 2 - 3X is 45. Therefore, the correct answer is (b) 45.

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If variance of x is 5, then find the variance of (2 – 3x)(a) 10(b) 45(c) 5(d) -13

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