Method of Moment Generating Function Help

In summary, the problem involves finding the probability function of Y, where Y is equal to the sum of X1 and n2 minus X2. The mgf of n2 - X2 is also needed to solve the problem. Additionally, it is unclear what n2 - X2 represents in terms of counting successes.
  • #1
wannabe92
9
0
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)?
 
Physics news on Phys.org
  • #2
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)?

If X2 counts the number of successes, what does n2 - X2 count?

RGV
 

FAQ: Method of Moment Generating Function Help

What is the method of moment generating function?

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.

How is the method of moment generating function helpful in statistics?

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.

What are the steps involved in using the method of moment generating function?

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

What types of distributions can be analyzed using the method of moment generating function?

The method of moment generating function can be used for both discrete and continuous distributions. However, it is most commonly used for continuous distributions.

Are there any limitations to using the method of moment generating function?

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.

Similar threads

MHB Derivation of snedecors F distribution
Replies
1
Views
3K
How Does the Probability of Failure Change in Synchronous Machine Operations?
Replies
2
Views
3K
I Finding vertex of a 3D Triangle on a Plane
Replies
3
Views
1K
Calculating ρ(Y,Z) for Independent Variables X1..Xn+Xn+1
Replies
5
Views
2K
Questions about Linear Combinations of Random Variables
Replies
4
Views
3K
Probability Function Homework: Solving Parts (d), (e) & (f)
Replies
1
Views
3K
The Probability Density of X^2?
Replies
5
Views
1K
MHB What Is the Success Probability of Merged Bernoulli Processes X1 and X2?
Replies
3
Views
2K
Calculating Variance of Y with X1, X2,...,X15
Replies
1
Views
1K
Data Generation with Requirement
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top