wannabe92 said:Let X1 be a binomial random variable with n1 trials and p1 = 0.2 and X2 be an independent
binomial random variable with n2 trials and p2 = 0.8. Find the probability function of
Y = X1 + n2 – X2.
Exactly how does one calculate the mgf of (n2 - X2)?
The method of moment generating function is a statistical technique used to find the parameters of a probability distribution. It relies on the property that the moments (i.e. mean, variance, etc.) of a distribution can be expressed in terms of the moment generating function.
The method of moment generating function is helpful in statistics because it allows for the estimation of parameters of a distribution without having to know the exact form of the distribution. It is also useful for finding the moments of a distribution, which can then be used to calculate other important statistics.
The steps involved in using the method of moment generating function are:
1. Find the moment generating function of the distribution
2. Expand the moment generating function in terms of its power series
3. Equate the coefficients of the power series to the corresponding moments of the distribution
4. Solve for the parameters of the distribution
The method of moment generating function can be used for both discrete and continuous distributions. However, it is most commonly used for continuous distributions.
Yes, there are some limitations to using the method of moment generating function. It may not be applicable for distributions with heavy tails or for distributions that do not have finite moments. Additionally, it may not always give accurate results for small sample sizes.