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Results tagged with moment-generating-function
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user 382603
A description of a probability distribution which is related to the Laplace transform. Use also for its logarithm, the cumulant generating function.
-2
votes
1
answer
80
views
Evaluating $E(x^{-1}). $
Could you please help me to prove the following equation:
$$E(x^{-1})=\int_{0}^{\infty}M_{x}(-t)dt$$
Where $M_{x}(-t)$ is the moment-generating function.
I think the following equation will be useful: …
- 41
1
vote
Accepted
Evaluating $E(x^{-1}). $
$$E\left(\frac{1}{x}\right)=\int_{-\infty}^{0}{e^{ux}du}=\int_{0}^{\infty}{e^{-ux}du}$$
$$E\left(\frac{1}{x}\right)=\int_{0}^{\infty}{x^{-1}f\left(x\right)dx=\int_{0}^{\infty}{\left(\int_{0}^{\infty}{ …
- 41
0
votes
1
answer
432
views
Expected value of Y = (1/X) where X is Gamma Distribution [closed]
Let's suppose
$$E\left(\frac{1}{x}\right)=\int_{0}^{\infty}{M_X(-t)dt}$$
Could you please help me to find
$$E\left(\frac{1}{x}\right)$$ where
$$X \sim\textrm{Gamma}(\alpha, \beta)$$ and $$E(X) = \alp …
- 41
0
votes
1
answer
100
views
Limiting value of the moment generating function
Suppose that the discrete random variable $X_{n}$has a geometric distribution given by
$$f_{X_n}(x_n)=P_n{(1-P_n)}^{x_n}$$ where $$x_n={0,1,2,3,}$$ and $$P_n\ =\ \frac{\lambda}{n}$$ for $0<\lambda<n$. …
- 41