X is a random variable with an exponential distribution with rate= 0.7 Thus the pdf of X is f(x) =e^x

for 0x where= 0.7.

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 ofX^0.2

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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 .33X1

e) Calculate the probability that X > 0.15 by using the pexp function

f) Calculate the probability that X is at least 1.5 more than its expected value. Use the pexp function

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