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.

output gl - {4. 2, 5, 1, 3} 82 - (7, 3. 2, 9. 5} #3 - {5, 8, 3, 2, 4} (#1 - 62) u (62 - 81) = {4. 1, 7. 9} (#1 u s2) - (81 n #2) = {4. 1, 7, 9} Is (81 - 82) n (82 - al) empty? true Are al n (82 u s3) and (al n 82) u (al n #3) equal? true Are (al n 82) u (82 n #3) and (al u a]] equal? false Is (s1 - 82) a subset of 827 false Is (81 - 82) u (82 n 83) a subset of a17 true In (81 - 82) u (82 n $3) a proper subset of al? false Max element in al = 5 Max element in 82 - 9 Max element in 83 = B 51 - {D, B, A, E, C} $2 - {G, I, C. B, E} 13 = {F. C, H, B, D} (81 - 62) u (82 - #1) = {D, A, G. I} (al u s2) - (81 n #2) = {D, A, G. I} Is (al - 82) n (82 - 81) empty? true Are sl n (82 u 83) and (sl n 82) u (al n $3) equal? true Are (8l n #2) u (82 n 83) and (al u s3) equal? false Is (s1 - 82) a subset of s2? false Is (s1 - 82) u (82 n #3) a subset of s1? true Is (#1 - 82) u (82 n 83) a proper subset of al? true Max element in s1 = E Max element in 82 = I Max element in #3 = H 81 = {Gina, Bob, Jim, Anna, Mary} 82 = {Tom, Hal, Mary, Bob, Anna} 83 = {Hal, Mary, Bob, Sara, Gina} (s1 - #2) u (82 - s1) = {Gina, Jim, Tom, Hal} (s1 u 82) - (81 n #2) = {Gina, Jim, Tom, Hal} Is (81 - 82) n (82 - 81) empty? true Are s1 n (82 u s3) and (s1 n #2) u (#1 n #3) equal? true Are (s1 n $2) u (82 n s3) and (sl u 83) equal? false Is (s1 - 82) a subset of $2? false Is (s1 - 82) u (82 n 83) a subset of sl? false Is (s1 - 82) u (82 n #3) a proper subset of s1? false Max element in s1 = Mary Max element in s2 = Tom Max element in 83 = Sara15. Suppose that X, Y and Z are normally distributed where X = $100,100), Y z M400, 400) and