Question

Problem #3. X is a random variable with an exponential distribution with rate λ = 7 Thus the pdf of X is f(x) = λ e^−λx for 0 ≤ x where λ = 7.

a) Using the f(x) above and the R integrate function calculate the expected value of X.

b) Using the f(x) above and the R integrate function calculate the expected value of X²

c) Using the dexp function and the R integrate command calculate the expected value of X.

d) Using the pexp function find the probability that .2 ≤ X ≤ .4

e) Calculate the probability that X > .2. Use the pexp function

f) Calculate the probability that X is at least .3 more than its expected value.Use the pexp function

g) Copy your R script for the above into the text box here.

Answer 1