Question

Let X and Y be independent random variables each with Geom(0.12) distribution and let N = X + Y. Find the joint pmf of (X, N) P(X = m, N = n) = for 0 ? m ? n < ?. Hint: {X = m, N = n} = {X = m, Y = n - m} Find the pmf of N P(N = n) = for 0 ? n < ?. Find the conditional pmf of X given N = n P(X = m|N = n) = for 0 ? m ? n < ?. Do you recognize this distribution? It is a named distribution.

          Let X and Y be independent random variables each with Geom(0.12) distribution and let N = X + Y.

Find the joint pmf of (X, N)
P(X = m, N = n) = for 0 ? m ? n < ?. Hint: {X = m, N = n} = {X = m, Y = n - m}

Find the pmf of N
P(N = n) = for 0 ? n < ?.

Find the conditional pmf of X given N = n
P(X = m|N = n) = for 0 ? m ? n < ?.

Do you recognize this distribution? It is a named distribution.

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Let X and Y be independent random variables each with Geom(0.12) distribution and let N = X + Y.

Find the joint pmf of (X, N)
P(X = m, N = n) = for 0 ? m ? n < ?. Hint: X = m, N = n = X = m, Y = n - m

Find the pmf of N
P(N = n) = for 0 ? n < ?.

Find the conditional pmf of X given N = n
P(X = m|N = n) = for 0 ? m ? n < ?.

Do you recognize this distribution? It is a named distribution.

Added by Gema Y.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Let X and Y be independent random variables, each with a Geom(0.12) distribution, and let N = X + Y. Find the joint pmf of (X, N), P(X = m, N = n) for 0 ≤ m ≤ n < ∞. Hint: {X=m,N=n}={X=m,Y=n-m} Find the pmf of N, P(N = n) for 0 ≤ n < ∞. Find the conditional pmf of X given N = n, P(X = m | N = n) for 0 ≤ m ≤ n < ∞. Do you recognize this distribution? It is a named distribution.

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