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

= 3^{2}

= sqrt ( var(y) )

= sqrt ( 3^{2} )

= **3**

b)

V = 9X

= E(V)

= E(9X )

= 9 E(X)

= 9 * 10

= **90**

Var(V) = Var(9X )

= 9^{2} Var(X)

= 9^{2} * 3^{2}

= 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 )

= 9^{2} Var(X) + 0

= 9^{2} * 3^{2}

= 729

= sqrt ( var(W) )

= sqrt ( 729 )

= **27**

The mean and standard deviation of a random variable x are 7 and
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(1) y=x+1 μ= σ=
(2) v=8x μ= σ=
(3) w=8x+1 μ= σ=

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