Answer to Question #87018 in Statistics and Probability for Swati malik

Question #87018
In a certain Poisson frequency distribution the frequency corresponding to 3 successes is one - third the frequency corresponding to 4 successes. Find its mean and standard deviation.
1
Expert's answer
2019-03-26T12:12:43-0400

The Poisson probability is


"P(X=k)={{e^{-\\lambda}*\\lambda^k} \\over {k!}}"

The frequency corresponding to 3 successes is


"P(X=3)={{e^{-\\lambda}*\\lambda^3} \\over {3!}}"

The frequency corresponding to 4 successes is


"P(X=4)={{e^{-\\lambda}*\\lambda^4} \\over {4!}}"

Given that the frequency corresponding to 3 successes is one-third the frequency corresponding to 4 successes


"{{P(X=3)} \\over {P(X=4)}}={1 \\over 3}"

"{{e^{-\\lambda}*\\lambda^3*4!} \\over {e^{-\\lambda}*\\lambda^4*3!}}={1 \\over 3}"

"\\lambda =12"

The mean of the distribution is


"\\mu=\\lambda=12"

The variance of the distribution is


"Var(X)=\\sigma^2=\\lambda=12"

The standard deviation is


"\\sigma=\\sqrt{12}=2\\sqrt{3}"



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