AP EAMCET · Maths · Probability
If \(X\) is a poisson variable such that \(3 P(X=4)=\frac{1}{2} P(X=2)+P(X=0)\), then the mean \(X\) is
- A 1
- B 2
- C \(\frac{3}{2}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Given, \[ 3 P(X=4)=\frac{1}{2} P(X=2)+P(X=0) \] \(X\) is poisson distribution this gives \[ P(X=x)=\frac{e^{-\lambda} \lambda^x}{x !}, \quad[x=0,1,2, \ldots] \] Now, \(3 P(X=4)=\frac{1}{2} P(X=2)+P(X=0)\)…
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