\therefore \quad Standard deviation =\sqrt{\mu_{2}}=c.Example ... | Filo

SOLVED:Consider the rv X= time headway in Example 3.5 . (a) Find the moment generating function and use it to find the mean and variance. (b) Now consider a random variable whose pdf is f(x)={ .15 e^-.15 x x ≥ 0 0 otherwise. 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-.5 and use the relationship for linear functions Ma X b(t)=e^b t MX(a t) to obtain the mgf of Y from (a). Comp