A fair 4 sided die is rolled.
The random variable X(s) outputs -1 if the roll is 2; and 4 if the roll is 1, 3, or 4.
Now, when the 4 sided die is rolled, the possible outcomes are {1,2,3,4}.
So, there are 4 all possible cases.
Now, the outcomes are equally likely.
This means
This means,
X(s) takes value -1 with probability of 1/4.
X(s) takes value 4 with probability of 3/4.
Now, we have to find the value of
This is nothing but the Moment Generating Function of X.
According to its definition, we know
Where, x is the value X takes and P(X=x) is the corresponding probability.
Ths becomes
Thus the answer is
The Moment Generating Function of X is
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