A description of a probability distribution which is related to the Laplace transform. Use also for its logarithm, the cumulant generating function.
Questions tagged [moment-generating-function]
283 questions
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Finding the limiting distribution using moment generation functions
Question: Let $Z_{i}$ ~ $N(0,1)$ be independent random variables for i = 1,2,... . Obtain the limiting distribution of $$\frac{1}{\sqrt{n}}\Bigl(\sum_{i=1}^n\Bigl(Z_{i} + \frac{1}{n}\Bigr)\Bigr)$$ using moment generating functions.
So far I have:…
emmasdfghjkl
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Help on Moment Generating Functions
I have recently been given a set of practice problems for my probabilities course and I have no idea where to even start on this question.
The distribution of X = the number of toppings ordered by a randomly selected customer is given in the table…
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Moment generating function interval on which is defined
I have a simple question about moment generating functions(MGFs).
Does the interval on which a MGF is defined corresponds to the support of the random variable?
For instance, considering a standard logistic density function
$f(x)=…
Maximilian
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Exam question about compound distributions and MGFs
Studying for a test in course about stochastic processes, here's a test question that I can't fully understand:
An insurance company insures its policyholders against damages of a particular kind. Damages of this kind are reported by the…
user331219
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Moment Generating Function for values $t \neq 0$
I'm studying statistics using Rice's Mathematical Statistics and Data Analysis.
We can find the $r$th moment of a random variable $X$ by taking the moment generating function $M(t)$ of $X$ and taking the derivative $r$ times. Then substituting…
Snowball
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Moment generating function between 2 variables
I understand that mean of Y is M'Y(0), whereas variance of Y is M''Y(0).
I can derive expressions through differentiation to get M'Y(0) and M''Y(0). The 2, however, have the expression Mx(0) in them.
How do I get Mx(0) from the fact that M'x(0)is μ…
zingertek
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How to find the support of MGF
I am having a difficult time determining the support or range of a MGF for a given pmf. The specific questions states to find the MGF of f(x)=6/((x^2)(pi^2)) for x=1,2,3...
The result (which is the same answer on the prof's answer key) is
(6/pi^2)…
cb12991
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