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The distance, X, between flaws on a long cable has an exponential distribution with a parameter Thus, the density of X is: d) for 0x001 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(). gexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with defined as above or with dexp() for all parts. a) What is the expected value of X? b) What is the variance of X? c) What is the standard deviation of X? A is what R calls rate.

The distance, X, between flaws on a long cable has an exponential distribution with a parameter Thus, the density of X is: d) for 0x001 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(). gexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with defined as above or with dexp() for all parts. a) What is the expected value of X? b) What is the variance of X? c) What is the standard deviation of X? A is what R calls rate.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The distance, X, between flaws on a long cable has an exponential distribution with a parameter λ = f(x, 2) = 2 e-ix for 0 ≤ x ≤ 00, λ = 12 a) What is the expected value of X? 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(), gexp()) 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. b) What is the variance of X? c) What is the standard deviation of X? is what R calls rate. d) What is the probability that X is larger than its expected value? e) What is the probability that X is > 5? f) What is the probability that X is > 10? . Thus, the density of X is: g) What is the probability that X > 10 given that X > 5? h) What is the median of X?
Transcribed Image Text:The distance, X, between flaws on a long cable has an exponential distribution with a parameter λ = f(x, 2) = 2 e-ix for 0 ≤ x ≤ 00, λ = 12 a) What is the expected value of X? 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(), gexp()) 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. b) What is the variance of X? c) What is the standard deviation of X? is what R calls rate. d) What is the probability that X is larger than its expected value? e) What is the probability that X is > 5? f) What is the probability that X is > 10? . Thus, the density of X is: g) What is the probability that X > 10 given that X > 5? h) What is the median of X?
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