Question:

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

for 0 ? x 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 of X0.2

.

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 .33 ? X ? 1

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.

Problem 2: Please check whether each of the following processes is Recurrent Nonnull or not. (1) A birth and death process with rates H An = 1+ n +1 I