Consider the rv X = hazardous flood rate in Example 4.5.
a. Find the moment generating function and use it to find the mean and variance.
b. Now consider a random variable whose pdf is

Find the moment generating function and use it to find the mean and variance. Compare with (a), and explain the similarities and differences.
c. Let Y = X − 10 and use the relationship for linear functions M_aX+b(t) = e^btM_X(at) to obtain the mgf of Y from 

(a). Compare with the result of 

(b) And explain.

Data From Example 4.5

Transcribed Image Text:

f(x) = .04e-.04x x>0