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Distributionsmedium
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Let XXX be a random variable representing the number of failures before the first success in a sequence of Bernoulli trials with probability of success ppp. If XXX follows a Geometric distribution P(X=k)=(1−p)kpP(X=k) = (1-p)^k pP(X=k)=(1−p)kp for k=0,1,2,…k=0, 1, 2, \dotsk=0,1,2,…, what is the variance Var(X)Var(X)Var(X)?