1 Answer

Given independent random variables, X and Y, with means and standard deviations as shown, find the mean

3748 Views

0

Votes

1 Answer

Given independent random variables, X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the variables in parts a to d.

	mean	SD
X	100	13
Y	15	3

a. 5X

b. Y + 3

c. X + Y

d. X - Y

0

tutor

tutor Added an answer on Jul 05,2019

a) 5 X

Note that the expected value is 5 * E(X) = 5*100 = 500

The standard deviation of the variable is sqrt(k^2 * var(x))

sqrt(13^2 * 25) = 65.

b.

E(Y + 3) = E(Y) + 3 = 15+3 = 18

SD(Y + 3) = SD(Y)

SD(Y+3) = 3

c. c) Find the mean and standard deviation for the random variable X + Y.

E(X+Y) = E(X) + E(Y) = 100 + 15 = 115

SD(X + Y) = sqrt(var(X) + var(Y))

SD = sqrt(13^2 + 3^2) = 13.34

d) Find the mean and standard deviation for the random variable X - Y.

E(X - Y) = 15 - 100 = -85

SD(X - Y) = sqrt(var(X) + var(Y) = 13.34

Reply

Given independent random variables, X and Y, with means and standard deviations as shown, find the mean

A PHP Error was encountered