- Now Consider The Following Probability Distribution For The Number Of Motorcycles Per Family Y Y 0 1 F Y 0 5 0 5 D 1 (52.93 KiB) Viewed 80 times
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- Now Consider The Following Probability Distribution For The Number Of Motorcycles Per Family Y Y 0 1 F Y 0 5 0 5 D 2 (100.55 KiB) Viewed 80 times
2. Suppose the population/probability distribution for random variable X, the number of cars a family owns, is: X 0 1 2 3 f(x) 0.35 0.4 0.15 0.1 This means, for example, that 20 percent of families do not own a car, 40 percent of families have 1 car, etc. (a) What is the mean or expected number of cars, i.e. E[X] or ux? (b) Using the formula E[(x-ux)], calculate the variance of the number of cars, i.e. Var(x) or o? (c) Using the alternative formula E[X2] – E[X] to recalculate variance, confirm you get the same answer as (b). Now consider the following probability distribution for the number of motorcycles per family, Y: Y 0 1 f(Y) 0.5 0.5 (d) What is the mean or expected number of motorcycles, i.e. E[Y] or my? (e) What is the variance of the number of motorcycles, i.e. Var(Y) or o? (f) Let V = X+Y be the number of vehicles owned by a family. What is the expected number of vehicles owned by a family, E(V)? (g) What is Var(V)? Assume X and Y are independent. (h) Let W = 4x + 2y be the number of wheels in a family's garage. What is E(W)? (i) What is Var(W)?