The special case of the gamma distribution in which a isa positive integer n is called an Erlang distribution. If wereplace b by 1/l in Expression (4.8), the Erlang pdf isf(x; l, n) 5 5l(lx)n21e2lx(n 2 1)! x $ 00 x , 0It can be shown that if the times between successiveevents are independent, each with an exponential distributionwith parameter l, then the total time X thatelapses before all of the next n events occur has pdff(x; l, n).a. What is the expected value of X? If the time (in minutes)between arrivals of successive customers isexponentially distributed with l 5 .5, how muchtime can be expected to elapse before the tenth customerarrives?b. If customer interarrival time is exponentially distributedwith l 5 .5, what is the probability that thetenth customer (after the one who has just arrived)will arrive within the next 30 min?c. The event {X # t} occurs iff at least n events occurin the next t units of time. Use the fact that the numberof events occurring in an interval of length t hasa Poisson distribution with parameter lt to write anexpression (involving Poisson probabilities) for theErlang cdf F(t; l, n) 5 P(X # t).

STA 215 Chapter 8 Regression Wisdom Looking at residuals is the easiest way to check for linearity. Residuals reveal subtleties not apparent from the scatterplot. They can also help us focus on the appropriateness of the regression line. Example: Below is a scatter plot of the Dive Heart...