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.

Step-by-step explanation:

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

x-11012Total

p0.30.10.50.11

xp-0.310.50.21.4

x^2p0.3100.50.411.2

Mean of X = 1.4

Var(x) = 11.2-1.4^2 =  9.24    

y235  

p0.60.30.1  1

yp1.20.90.502.6

y^2p2.42.72.507.6

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

she will travel a distance in the range of 3 - 11 miles