Question

Assume X and Y are independent random variables with the following distributions:

Col1 X -1 10 1 2
Col2 P(X) 0.3 0.1 0.5 0.1

Col1 Y 2 3 5
Col2 P(Y) 0.6 0.3 0.1 18.

1. Find the mean, variance, and standard deviation of X.
2. Find the mean, variance, and standard deviation of Y.
3. Let W = 3 + 2 X. Find the mean, variance, and standard deviation of W.

Answer 1

Explanation:

Given that X and Y are independent random variables with the following distributions:

x -1 10 1 2 Total

p 0.3 0.1 0.5 0.1 1

xp -0.3 1 0.5 0.2 1.4

x^2p 0.3 10 0.5 0.4 11.2

Mean of X = 1.4

Var(x) = 11.2-1.4^2 = 9.24

y 2 3 5

p 0.6 0.3 0.1 1

yp 1.2 0.9 0.5 0 2.6

y^2p 2.4 2.7 2.5 0 7.6

Mean of Y = 2.6

Var(Y) = 11.2-1.4^2 = 0.84

3) W=3+2x

Mean of w =3+2*Mean of x = 7.2

Var (w) = 0+2^2 Var(x)= 36.96