Mathematics, 30.11.2019 05:31 loloroyroy264

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?

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Answer from: 1hannacarson

$F_{T}(t)=\frac{1}{2} +\frac{1}{2}(1-e^{-\lambda t})$

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:

$P(X=x)=\lambda e^{-\lambda x}$

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 $t\geq 0$ the CDF for the waiting time is given by:

$F_{T}(t) =P(T\leq t)$

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:

$F_{T}(t)=P(T\leq t|0 customers)P(0 customers)+ P(T\leq t|1 customers)P(1 customers)$

On this case the probability that we need to wait if we have o customers ahead is $P(T\leq t|0 customers)=1$ 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 $P(0 customers)=P(1 customers)=\frac{1}{2}$ . And replacing we have:

$F_{T}(t)=\frac{1}{2} +\frac{1}{2}\int_{0}^{t} \lambda e^{-\lambda \tau} d\tau = \frac{1}{2}+\frac{1}{2}[-e^{-\lambda t}+e^{-\lambda 0}]= \frac{1}{2} +\frac{1}{2}(1-e^{-\lambda t})$

Answer from: Quest

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

Need 45 ! compare the rates at which each of the three students read: which student read at a fa

Answer from: Quest

step-by-step explanation:

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