- #1
EngWiPy
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Hello,
Suppose that the Cumulative Distribution Function (CDF) of a random variable X is [tex]F_X(x)[/tex], which is by definition is:
[tex]F_X(x)=\text{Pr}\left[X\leq x\right]=\text{Pr}\left[\frac{1}{X}\geq \frac{1}{x}\right]=1-\text{Pr}\left[\frac{1}{X}\leq \frac{1}{x}\right]=1-F_{1/X}\left(1/x\right)[/tex]
Considering this relation between the CDF of X and the CDF of its reciprocal, what is the relation between the Moment Generating Function (MGF) of X and its reciprocal?
Any help will be highly appreciated.
Thanks in advance
Suppose that the Cumulative Distribution Function (CDF) of a random variable X is [tex]F_X(x)[/tex], which is by definition is:
[tex]F_X(x)=\text{Pr}\left[X\leq x\right]=\text{Pr}\left[\frac{1}{X}\geq \frac{1}{x}\right]=1-\text{Pr}\left[\frac{1}{X}\leq \frac{1}{x}\right]=1-F_{1/X}\left(1/x\right)[/tex]
Considering this relation between the CDF of X and the CDF of its reciprocal, what is the relation between the Moment Generating Function (MGF) of X and its reciprocal?
Any help will be highly appreciated.
Thanks in advance