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Suppose the time in minutes, X, that a customer stays in a store has an exponential distribution with a mean of 5 minutes. Thus, the density of X is f(x,x)= λ ex for 0 ≤ x ≤ co. λ is what R calls rate. Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answer parts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all par a) What is the value of 2? b) What is the variance of X? c) What is the standard deviation of X? d) What is the probability that X is greater than its expected value? e) What is the probability that X is> 4? [ f) What is the probability that X is > 8?

Suppose the time in minutes, X, that a customer stays in a store has an exponential distribution with a mean of 5 minutes. Thus, the density of X is f(x,x)= λ ex for 0 ≤ x ≤ co. λ is what R calls rate. Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answer parts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all par a) What is the value of 2? b) What is the variance of X? c) What is the standard deviation of X? d) What is the probability that X is greater than its expected value? e) What is the probability that X is> 4? [ f) What is the probability that X is > 8?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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Suppose the time in minutes, X, that a customer stays in a store has an exponential distribution with a mean of 5 minutes. Thus, the density of X is f(x,^) = λ e-^x for 0≤ x ≤co. A is what R calls rate. Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answer parts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts. a) What is the value of λ? b) What is the variance of X? c) What is the standard deviation of X? d) What is the probability that X is greater than its expected value? e) What is the probability that X is > 4? f) What is the probability that X is > 8? g) What is the probability that X > 8 given that X > 4? h) What is the median of X?
Transcribed Image Text:Suppose the time in minutes, X, that a customer stays in a store has an exponential distribution with a mean of 5 minutes. Thus, the density of X is f(x,^) = λ e-^x for 0≤ x ≤co. A is what R calls rate. Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answer parts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts. a) What is the value of λ? b) What is the variance of X? c) What is the standard deviation of X? d) What is the probability that X is greater than its expected value? e) What is the probability that X is > 4? f) What is the probability that X is > 8? g) What is the probability that X > 8 given that X > 4? h) What is the median of X?
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g) What is the probability that X > 8 given that X > 4? 

h) What is the median of X? 

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