Question

If Y has a binomial distribution with n trials and probability of success p, the moment-generating function for Y is m(t) = (pet + )", where - 1 - p. Use the uniqueness of moment-generating functions to give the distribution of a random variable with moment-generating function m(t) - (0.6e! +0.4) The distribution is --Select--- , with n = and p =

Answer 1

The random variable with moment-generating function m(t) = (0.6e^t + 0.4)^n has a binomial distribution, with the probability of success p = 0.6. The number of trials n isn't specified but can be determined with additional context.

Step-by-step explanation:

When a random variable Y has a binomial distribution with n trials and probability of success p, the moment-generating function (mgf) is given by m(t) = (pe^t + q)^n, where q = 1 - p. Given the mgf m(t) = (0.6e^t + 0.4)^n, we can equate the coefficients of the corresponding terms to find p and q, which suggests that p = 0.6 and q = 0.4. Thus, the distribution of this random variable is a binomial distribution, with parameters n and p = 0.6. The value of n is not directly provided by the mgf, but if the context or question provides further information, it can be determined.