Let the waiting time of a bus on a day as T (in minutes). Assume on weekdays (fr

Question

Let the waiting time of a bus on a day as T (in minutes). Assume on weekdays (from Monday to Friday), T is an exponential random variable with mean 3 minutes; while on weekends (Saturday and Sunday), T is an exponential random variable with mear 5 minute:s (a) Find the pdf (probability density function) of T on an arbitrary day, i.e., the date is randomly picked. (b) Find the expected value of T (c) Find the variance ofT (c) E[T2E1] = Var(TE1] + (ETEq])2 = 9 + 32-18 (1 pt) E[T2l&J; = Var[TI&J; + (E(TIE 2])2 = 25 + 52 = 50 (1 pt) 2 190 7 (25)2 = 705 (1 pt) 190 var[7] = E[H]-E2 [7] =-(2) 2 = 749 (1 pt) I don't understand the answer in yellow, please explain in detail how do they come up with tha

Explanation / Answer

Var(Y) = E(Y^2) - (E(Y))^2 or

E(Y^2) = Var(Y) + (E(Y))^2

here

Y = T |E1 in first case

= T |E2 in second case

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