Suppose that cars arrive as a Poisson process with rate ₁ = 3 per minute and trucks arrive as a Poisson process with rate ₂ = 1 per minute.

Suppose that each car has a random weight with mean ₁ and variance ₁ ², each truck has a random weight with mean ₂ and variance ₂ ², and suppose that the weights for all vehicles are independent of each other.

(a) Let S be the total weight for vehicles arrived before time t = 10. Compute the expectation and the variance for S.

(b) Let Q be the total weight for cars that arrive before the first truck. Compute the expectation and the variance for Q.