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(Solved): If X1,,Xn are independent identically distributed geometric random variables with density ...

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If

X_{1}, \dots, X_{n}

are independent identically distributed geometric random variables with density

θ (1 - θ)^{x - 1} I_{{1, 2, \dots}} (x)

, what is the distribution of

X_{1} + \dots + X_{n}

?

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The sum of independent identically distributed (i.i.d.) geometric random variables follows a negative binom...

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