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For a Poisson variate X, P(X = 1) = P(X = 2). What is the mean of X?
- a)1
- b)3/2
- c)2
- d)5/2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
For a Poisson variate X, P(X = 1) = P(X = 2). What is the mean of X?a)...
Solution:
Given, P(X=1) = P(X=2)
Let the probability of X=k be P(X=k)
Then, P(X=1) = P(X=2) = P(X=k) (let)
Using probability mass function of Poisson distribution, we get
P(X=k) = (e^(-λ) * λ^k)/k!
where λ is the mean of X.
Therefore, (e^(-λ) * λ^1)/1! = (e^(-λ) * λ^2)/2!
2λ = λ^2
λ(λ-2) = 0
λ = 0 or λ = 2
Since λ cannot be zero, the mean of X is λ = 2.
Hence, option (c) is the correct answer.
Given, P(X=1) = P(X=2)
Let the probability of X=k be P(X=k)
Then, P(X=1) = P(X=2) = P(X=k) (let)
Using probability mass function of Poisson distribution, we get
P(X=k) = (e^(-λ) * λ^k)/k!
where λ is the mean of X.
Therefore, (e^(-λ) * λ^1)/1! = (e^(-λ) * λ^2)/2!
2λ = λ^2
λ(λ-2) = 0
λ = 0 or λ = 2
Since λ cannot be zero, the mean of X is λ = 2.
Hence, option (c) is the correct answer.
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For a Poisson variate X, P(X = 1) = P(X = 2). What is the mean of X?a)1b)3/2c)2d)5/2Correct answer is option 'C'. Can you explain this answer?
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