Answer to Question #88350 in Statistics and Probability for Shivam Nishad

Question #88350
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
2019-04-24T11:38:04-0400

P(X=3)=13P(X=4)eλλ33!=13eλλ44!λ=34!3!=12Mean=Variance=λ=12Standard  deviation=12=23P(X=3)=\frac{1}{3}P(X=4)\\ e^{-\lambda}\frac{\lambda^3}{3!}=\frac{1}{3}e^{-\lambda}\frac{\lambda^4}{4!}\\ \lambda=\frac{3*4!}{3!}=12\\ Mean=Variance=\lambda=12\\ Standard\; deviation=\sqrt{12}=2\sqrt{3}


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