Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).
Assertion (A): Suppose that X has poisson distribution.
If $P(X = 3) =\frac{3}{4} P(X = 2)$, then mean of X is $\frac{9}{4}$.
Reason (R): The recurrence formula for poisson distribution is $P(r + 1) =\frac{λ}{r+1}P(r),r=0,1,2,3...$ where $λ = np$.
Select the correct answer from the options given below.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
We know that recurrence formula for poisson distribution is $P(r + 1) =\frac{λ}{r+1}P(r)$
∴ Reason is true.
Using recurrence formula, we have
$P(X = 3)=\frac{λ}{3}=P(X = 2)$.
Given $P(X = 3) =\frac{3}{4}P(X = 2)$
On comparing, we get
$\frac{λ}{3}=\frac{3}{4}⇒λ=\frac{9}{4}$
∴ Assertion is true.
Reason is the correct explanation of Assertion.