Question

if x is random variable,then var(2-3x) is
1. 2-var(3x)
2. var(2)-var(3x)
3. 2-3var(x)
4. 9var(x)

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If x is random variable,then var(2-3x) is

1. 2-var(3x)

2. var(2)-var(3x)

3. 2-3var(x)

4. 9var(x)

CONCEPT TO BE IMPLEMENTED

Mean

If X is a random variable corresponding to a random experiment then Arithmetic mean of X denoted by E(X) or by m and defined as m = E(X)

Variance

If X be a random variable corresponding to a random experiment then the variance of X, denoted by Var(X) and defined as

$\sf{Var (X ) = E {(X - m)}^{2} }$

Formula related to Variance

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

EVALUATION

USING FORMULA

$\sf{Var (2 - 3X ) }$

$\sf{ = {( - 3)}^{2} \: \: Var (X) }$

$\sf{ = 9 \: \: Var (X) }$

NOT USING FORMULA

(Using Definition)

Here

Mean

= E(2-3X )

= E(2) - 3 E(X)

= 2 - 3m

$\therefore \: \: \sf{Var (2 - 3X ) }$

$\sf{ =E{ \{(2 - 3X) - (2 - 3m) \}}^{2} }$

$\sf{ =E{ \{3(X - m) \}}^{2} }$

$\sf{ = {3}^{2} \: E{ \{(X - m) \}}^{2} }$

$\sf{ = 9 \: \: Var (X) }$

FINAL ANSWER

Hence the correct option is

If x is random variable,then var(2-3x) is

4. 9var(x)

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