In a Poisson distribution if P(x=4) = P(x= 5) then the parameter of Poissondistribution is:
Question
In a Poisson distribution if P(x=4) = P(x= 5) then the parameter of Poissondistribution is:
Solution
The parameter of a Poisson distribution is usually denoted by λ (lambda). The probability mass function of a Poisson distribution is given by:
P(X = k) = λ^k * e^-λ / k!
where:
- k is the number of occurrences of an event (the points in the distribution, in this case 4 and 5)
- λ is the expected number of occurrences (the parameter we're trying to find)
- e is the base of the natural logarithm (approximately equal to 2.71828)
- k! is the factorial of k
Given that P(X = 4) = P(X = 5), we can set up the following equation:
λ^4 * e^-λ / 4! = λ^5 * e^-λ / 5!
Solving this equation for λ gives us:
λ = 5
So, the parameter of the Poisson distribution is 5.
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