The following table represents the probability distribution of the discrete random variable X. The measure of the random variable x(E(x)) is:

The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. P(x, y) 1 2 0.015 0.010 0.025 1 0.030 0.020 0.050 2 0.075 0.050 0.125 3 0.090 0.060 0.150 0.060 0.040 0.100 0.030 0.020 0.050 What is the probability that there is exactly one car and exactly one bus during a cycle? What is the probability that there is at most one car and at most one bus during a cycle? What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = P(exactly one bus) = - Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflov during a cycle?

Consider the table below gives the probabilities of the distribution of random variable X. Value of X (x) P(X=x) (f(x)) 0 1 2 345 00 6 7 8 0.14 b C 0.10 0.13 0.13 d 0.02 0.01 In reference to the table, suppose that b = f(1) =0.15 and c = f(2)= 0.14. What is the probability P(2 ≤ X<7) equal to ?

The possible values of a discrete random variable X are 0, 1, 3, and 6 with respective probabilities 0.2, 0.3, 0.1, 0.4. Find E[X] and Var(X).