If n= 10, p=0 .2 for any binomial distribution then which one is the Moment generating function
Question
If n= 10, p=0.2 for any binomial distribution then which one is the Moment generating function
Solution
The moment generating function (MGF) of a binomial distribution is given by the formula:
M(t) = (q + pe^t)^n
where:
- n is the number of trials
- p is the probability of success on each trial
- q is the probability of failure on each trial (q = 1 - p)
- e is the base of the natural logarithm (approximately equal to 2.71828)
- t is the variable for which the MGF is calculated
Given that n = 10 and p = 0.2, we can substitute these values into the formula:
M(t) = (1 - 0.2 + 0.2e^t)^10 M(t) = (0.8 + 0.2e^t)^10
So, the moment generating function for a binomial distribution with n = 10 and p = 0.2 is (0.8 + 0.2e^t)^10.
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