Customers arrive at a facility according to a Poisson process N(t) of rate λ = 4.5 customers/hour. Each customer is admitted to the facility with probability p = 0.8. All customers, who are not admitted, leave and do not come back. Let X(t) be the number of customers admitted from time 0 to time t. Compute the following: (a) The mean value E[X(6.5)] = 23.4 (b) The probability P(X(6.5) = 23) = %. (c) The conditional probability P(X(6.5) = 23 | N(6.5) = 30) = %. Note: For parts (b) and (c), enter your answers as percentages but do not type the percent sign.

MATLAB: An Introduction with Applications
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Customers arrive at a facility according to a Poisson process N(t) of rate λ = 4.5 customers/hour. Each customer is
admitted to the facility with probability p = 0.8. All customers, who are not admitted, leave and do not come back. Let
X(t) be the number of customers admitted from time 0 to time t. Compute the following:
(a) The mean value E[X(6.5)] = 23.4
(b) The probability P(X(6.5) = 23) =
=
(c) The conditional probability P(X(6.5) = 23 | N(6.5) = 30) =
%.
%.
Note: For parts (b) and (c), enter your answers as percentages but do not type the percent sign.
Transcribed Image Text:Customers arrive at a facility according to a Poisson process N(t) of rate λ = 4.5 customers/hour. Each customer is admitted to the facility with probability p = 0.8. All customers, who are not admitted, leave and do not come back. Let X(t) be the number of customers admitted from time 0 to time t. Compute the following: (a) The mean value E[X(6.5)] = 23.4 (b) The probability P(X(6.5) = 23) = = (c) The conditional probability P(X(6.5) = 23 | N(6.5) = 30) = %. %. Note: For parts (b) and (c), enter your answers as percentages but do not type the percent sign.
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