Question

Suppose your waiting time for a bus in the morning is uniformly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time. What is the variance of the total waiting time?

Answer 1

Answer:

41/3

Step-by-step explanation:

given that your waiting time for a bus in the morning is uniformly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time.

Sum of both waiting times = X+Y

Where X = morning wait time is U(0.8) and

Y = evening wait time is U(0,10)

Since X and Y are independent

Var(x+y) = Var(x)+Var(y)

Var(x) = $\frac{8^2-0^2}{12} \\=\frac{16}{3}$

Var(Y) = $\frac{10^2-0^2}{12} \\=\frac{25}{3}$

Var(x+y) $\frac{16+25}{3} \\=\frac{41}{3}$