Iam waiting for two friends to arrive at my house. the time until a arrives is exponentially distributed with rate lambda(a) and the time until b arrives is exponentially distributed with rate lambda(b). once they arrive, both will spend exponentially distributed times, with respective rates u(a) and u(b) at my home before departing. the four exponential random variables are independent.

a) what is the probability that a arrives before and departs after b?

b) what is the expected time of the last departure?

Determine if the following statement is true or false. the normal curve is symmetric about its​ mean, mu. choose the best answer below. a. the statement is false. the normal curve is not symmetric about its​ mean, because the mean is the balancing point of the graph of the distribution. the median is the point where​ 50% of the area under the distribution is to the left and​ 50% to the right.​ therefore, the normal curve could only be symmetric about its​ median, not about its mean. b. the statement is true. the normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ therefore, the normal curve is symmetric about the​ mean, mu. c. the statement is false. the mean is the balancing point for the graph of a​ distribution, and​ therefore, it is impossible for any distribution to be symmetric about the mean. d. the statement is true. the mean is the balancing point for the graph of a​ distribution, and​ therefore, all distributions are symmetric about the mean.