Question 21:47. Let random variable X is follows Poisson distribution with parameter 2 then the recurrence relation between successive probabilities is P(X=X+1) = P(X=x) P(X=X+1) = P(X=x) P(X=X+1) = 1/x P(X=x) P(X=X+1) =N/x P(X=x)
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The formula for computing probabilities that are from a Poisson process is:
P\left(x\right)=\frac{{\mu }^{x}{e}^{-\mu }}{x!}
where P(X) is the probability of X successes, μ is the expected number of successes based upon historical data, e is the natural logarithm approximately equal to 2.718, and X is the number of successes per unit, usually per unit of time.
In order to use the Poisson distribution, certain assumptions must hold. These are: the probability of a success, μ, is unchanged within the interval, there cannot be simultaneous successes within the interval, and finally, that the probability of a success among intervals is independent, the same assumption of the binomial distribution.
Step-by-step explanation:
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