Calamity jane goes to the bank to make a withdrawal, and is equally likely to find 0 or 1 customers ahead of her. the service time of the customer ahead, if present, is exponentially distributed with parameter λ. what is the cdf of jane’s waiting time?

Step-by-step explanation:

The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

We are interested on the cumulative distribution function (CDF) of Jane’s waiting time. Let T the random variable that represent the Jane’s waiting time, and t possible value for the random variable T.

For the CDF for the waiting time is given by:

For this case we can use the total rule of probability and the conidtional probability. We have two options, find 0 or 1 customer ahead of Jane, and for each option we have one possibility in order to find the CDF, like this:

On this case the probability that we need to wait if we have o customers ahead is since if we don't have a customer ahead, so on this case Jane will not wait. And assuming that the probability of find 0 or 1 customers ahead of Jane is equal we have . And replacing we have:

dnji

step-by-step explanation:

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not enough information

step-by-step explanation:

we cannot know this, because the other students could have handed out 10 flyers, or they could have handed out 100. one way, the mean would go up, and another way, the mean would go down.