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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

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

 

 

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