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AP EAMCET20227 Jul 2022Evening ShiftMathematicsProbabilityActual

If X is a Poisson random variate with mean 3, then P(|X-3| < 2)=

Options

  1. A9 2 e^3
  2. B99 8 e^3
  3. C3 2 e^3
  4. D1 3 e^3

Correct answer

B. 99 8 e^3

Step-by-step solution

For poisson distribution, P(X=k)= ^k e^ - k ! aligned & Here, =3,|X-3| < 2 & 1 < X < 5 & X=2,3,4 & P( X-3) < 2)=P(X=2)+P(X=3)+P(X=4) & =e⁻³ [ 9 2 + 27 6 + 81 24 ]= 99 8 e^3 aligned

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