X is a random variable with an exponential distribution with rate=0.3. Thus the pdf of X is f(x) = ex for 0 ≤ x where λ = a) Using the f(x) above and the R integrate function calculate the expected value of X. 3.333333 f) Calculate the probability that X is at least 3 greater than its expected value. Use the pexp function 0.1495686 Using R script to get answers

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X is a random variable with an exponential distribution with rate=0.3. Thus the pdf of X is f(x) = 1 ex for 0 ≤ x where λ = 0.3.
a) Using the f(x) above and the R integrate function calculate the expected value of X. 3.333333
f) Calculate the probability that X is at least 3 greater than its expected value. Use the pexp function [0.1495686
Using R script to get answers
Transcribed Image Text:X is a random variable with an exponential distribution with rate=0.3. Thus the pdf of X is f(x) = 1 ex for 0 ≤ x where λ = 0.3. a) Using the f(x) above and the R integrate function calculate the expected value of X. 3.333333 f) Calculate the probability that X is at least 3 greater than its expected value. Use the pexp function [0.1495686 Using R script to get answers
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