Question

If V ar(X)=2, then V ar(8X+13)=?

Answer 1

then

example:

we have two x values.

x1 = 10

x2 = 20

Mean = 15,

Var (x) = 25.

first we are adding 5 units with each.

then new x value will be

x1 = 10+5 =15

x2 = 20 +5 =25

mean = 20.

Var(X+5) = 25.

if we add any numer to the X value the mean only change deviation will not change.

we multiply X value with 2.

new X value will be .

x1 = 10 *2=20

x2 = 20 * 2 =40

Mean = 30.

Var (2X) =100

that means 22 * Var(X) = 22 * 25 = 100.

so in our question.

Given data:

Var (x) = 2

then Var (8x+13) = Var (8x) = 82 var(X)

= 64*2

=128

var (8X+13 ) =128.