Question

The mean and standard deviation of a random variable x are 10 and 3 respectively. Find the mean and standard deviation of the given random variables:

(1) y=x+4

μ=

σ=

(2) v=9x

μ=

σ=

(3) w=9x+4

μ=

σ=

Answer 1

a)

y = x + 4

= E(Y)

= E(X + 4)

= E(X) + 4

= 10 + 4

= 14

Var(Y) = Var(X + 4)

= Var(X) + 0

= 3²

= sqrt ( var(y) )

= sqrt ( 3² )

= 3

b)

V = 9X

= E(V)

= E(9X )

= 9 E(X)

= 9 * 10

= 90

Var(V) = Var(9X )

= 9² Var(X)

= 9² * 3²

= 729

= sqrt ( var(V) )

= sqrt ( 729 )

= 27

c)

W = 9X + 4

= E(W)

= E(9X + 4)

= 9 E(X) + 4

= 9 * 10 + 4

= 94

Var(W) = Var(9X + 4 )

= 9² Var(X) + 0

= 9² * 3²

= 729

= sqrt ( var(W) )

= sqrt ( 729 )

= 27