The moment generating function of a random variable is $M _ { X } ( t ) = \frac { 1 } { 8 } e ^ { t } + \frac { 1 } { 2 } e ^ { 4 t } + \frac { 1 } { 4 } e ^ { 5 t } + \frac { 1 } { 8 } e ^ { 7 t }$ . Find P(X=i) for 1=1,…,7.

Question

Quizplus · Accepted Answer

The Answer is P(X=1)=1/8, P(X=4)=1/2, P(X=5)=1/4, P(X=7)=1/8, P(X=2)=P(X=3)=P(X=6)=1/8.

The Moment Generating Function of a Random Variable Is MX(t)=18et+12e4t+14e5t+18e7tM _ { X } ( t ) = \frac { 1 } { 8 } e ^ { t } + \frac { 1 } { 2 } e ^ { 4 t } + \frac { 1 } { 4 } e ^ { 5 t } + \frac { 1 } { 8 } e ^ { 7 t }MX​(t)=81​et+21​e4t+41​e5t+81​e7t

The Moment Generating Function of a Random Variable Is $M _ { X } ( t ) = \frac { 1 } { 8 } e ^ { t } + \frac { 1 } { 2 } e ^ { 4 t } + \frac { 1 } { 4 } e ^ { 5 t } + \frac { 1 } { 8 } e ^ { 7 t }$