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For each n > 1 let Xngeometric random variable with parameter A/n.Derive the cumulative distribution function F of Xn Find the mean E[X,] and the variance V(X,) ...

Question

For each n > 1 let Xngeometric random variable with parameter A/n.Derive the cumulative distribution function F of Xn Find the mean E[X,] and the variance V(X,) of X, For every 2 0, show that; lim P(X, < nt) = 1 - 2 4 ACoc

For each n > 1 let Xn geometric random variable with parameter A/n. Derive the cumulative distribution function F of Xn Find the mean E[X,] and the variance V(X,) of X, For every 2 0, show that; lim P(X, < nt) = 1 - 2 4 ACoc



Answers

For probability density function, over the given interval, find $E(x), E\left(x^{2}\right),$ the mean, the variance, and the standard deviation. $$f(x)=\frac{1}{\ln 4} \cdot \frac{1}{x}, \quad[0.8,3.2]$$

Mhm. The expectation of X equals the integral X times it's probability density function. So their cycles are integral from 0 to infinity. Eric's times 1/4 B to a power miners axle work for Dia. We should use the integration by parts. We know there's equals miners at times E. To the power miners X over four Plus injury go from 0 to Infinity than e. two power miners actual war fought dX So their sickles miners X miners whoa times each of power miners the axle Werfel them from their role to infinity As he goes. zero miners miners fall where she goes for next. We can build the expectation of X squared which is the NGO group X squared times it's probability density function. This equals the integral from 0 to infinity. Eric squared times 1/4 e. to the power of ads over four deer. Still we need to use the integration by parts and it's anti geographical functions miners X squared minus two X miners started to times E. To the power minus X over four. And it Echoes zero, Miners, 32. Hence the various egos, 32 miners four squared, which was 16. And the standard division is the square root of the variance, which is for.


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