The time required to obtain a building permit has an expecte

The time required to obtain a building permit has an expected value of 35 days, and a standard deviation of 17 days. After you have a building permit, you can call a contractor who will pour a foundation. The average time to wait for the foundation contractor to arrive and finish the job is 8 days, and the standard deviation is 2 days. When construction is busy, both the permit office and the foundation contractor take longer, so the covariance between the permit time and contractor wait time is 25 (days^2). What is the variance of the total time, which is just the sum of the two wait times? (This time should be given in days^2.)

You roll one red die and one black die. Both dice have 6 sides. They do not affect each other, so their covariance is zero. You\'ll win 3 dollars times the number of dots rolled on the red die, and lose 4 dollars times the number of dots rolled on the black die. What is the variance of your net winnings? (Hint: Variance of number of dots on a 6-sided die roll is 2.92)

For the die problem above, what\'s the standard deviation of your winnings?

Solution

A.) Var(T1) = 17^2 = 289 days^2

Var(T2) = 2^2 = 4 days^2

Var(Total Time) = Var(T1) + Var(T2) + 2*Cov(T1,T2)

= 289 + 4 + 2*(25) days^2

= 343 days^2

B.) Winnings = 3*R - 4*B

Var(R) = Var(B) = 2.92

So Var(Winnings) = 3^2*Var(R) + 4^2*Var(B)

= 9*Var(R) + 16*Var(B)

= 9*2.92 + 16*2.92

= 25*2.92

= 73

So Var(Winnings) = 73

So standard deviation(winnings) = sqrt(73) = 8.544