If x is a Poisson variate with P(x = 0) = P(x =1) = K then show that K=K =1/e.
Added by Brian E.
Step 1
Given that P(x=0) = P(x=1) = K, we can set up two equations: K = (λ^0 * e^(-λ)) / 0! = e^(-λ) K = (λ^1 * e^(-λ)) / 1! = λ * e^(-λ) Solving for λ in the second equation, we get: λ = K / e^(-λ) Substituting this into the first equation, we get: K = e^(-λ) = Show more…
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