Solve each problem on a separate sheet of paper. Show all necessary solut Let X denotes the percentage of time out of a 40-hour workweek that a call center agent is directly serving a client by answering phone calls. Suppose that X has a probability density function defined by f(x)= 3x2 for 0 < x<1. Find the mean and variance of X. Interpret the 1. results. ad ed bluov 3 intionofthedensityfunstion given by f(x)=-x(2-x)

What is the correct response to this question? Thanks.

the driving time from toronto to montreal are uniformly distributed with times ranging from four hours to 5.75 hours. draw a probability density graph that shows this (be sure to fully label your graph).

Students arrive at a lecture theatre independently. Suppose the number of students arriving in an hour follows a Poisson distribution with mean 10. Let 7 (in hours) be the time required to wait for 5 students to arrive. Derive the probability density function of T.

Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.

Let X be a random variable that follows the beta distribution. This random variable is continuous and is defined over the interval from 0 to 1. The probability density function is given by                                         whereand are integers, whose values determine the shape of the probability density function. Because X varies between 0 and 1, we can think of X as the probability that some event (say) E occurs or the proportion of times an event occurs in some population. For example, E could denote the event that a critical part in a newly designed car will lead to a catastrophic failure in accidents at high speeds.   The expected value (i.e., mean) of this random variable is []. That is,                                             . The Excel commands for the beta random variable are           =beta.dist(x,,,true,0,1) for the cumulative probability distribution, and           =beta.dist(x,,,false,0,1) for the probability density function. (a) Now, think in Bayesian terms.…