Question

If a random variable X has mean 3
and standard deviation 5, then the
variance of variable Y=2x - 2 is:​

Answer 1

SOLUTION

GIVEN

A random variable X has mean 3 and standard deviation 5

TO DETERMINE

The variance of variable Y = 2x - 2

FORMULA TO BE IMPLEMENTED

$\sf{1. \: \: Standard \: Deviation = + \sqrt{Var( X)} }$

$\sf{2. \: Var(a X + b) = {a}^{2} \: Var( X) \: }$

EVALUATION

Here it is given that A random variable X standard deviation 5

$\sf{ Var X = {5}^{2} = 25}$

So the variance of the variable Y

$= \sf{Var(Y) \: }$

$= \sf{Var(2X - 2) \: }$

$= \sf{ {2}^{2} \times Var(X) \: }$

$= \sf{ 4 \times Var(X) \: }$

$= \sf{ 4 \times 25 \: }$

$= \sf{ 100 \: }$

FINAL ANSWER

Hence the variance of the variable Y = 100

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