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pdf of the geometric distribution is f(x) = p q^(x-1) , x =1,2,...
where q = 1-p
find E(X2),
rewrite E(X2) as E[X(X-1)] +E[X]
use the value of the mean,E[X] =1/p refer mean of geometric distribution
expand the summation for E[X(X-1)] and use the binomial series
for [(1-u) ^ (-3)] adjusting for the 1/2
Then use the formula variance =E(X2) - [E(X)]2
answer and some steps are given below
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index of derivations and problems in statistics -------- derivations and problems in statistics
mean of the geometric distribution ---------mean of the geometric distribution
mean of the poisson distribution ------mean of the poisson distribution
mean and variance of the discrete uniform distribution f(x) = 1/k , x = 1,2,...k mean and variance of discrete uniform
other problems on applications of integration like area ,volume etc
integration formulae
problems on integration
**
list of formulae and notes on some math topics
collection of revision questions
formulae on sequences and series
(trig. formulae)
(integration formulae)
(other math problems without classification) or problem index
(formulae on differentiation)
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