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AP EAMCET2010MathematicsProbability

Suppose that a random variable X follows Poisson distribution. If P(X=1)=P(X=2) then P(X=5) is equal to

Options

  1. A2 3 e⁻²
  2. B3 4 e⁻²
  3. C4 15 e⁻²
  4. D7 8 e⁻²

Correct answer

C. 4 15 e⁻²

Step-by-step solution

Let be the mean of the poisson variate x . Then, P(X=r)= ^r e^ - r ! , r=0,1,2, Now, P(X=1)=P(X=2) e^ - 1 ! = ^2 e^ - 2 ! =2 Hence, P(X=5)= ^5 e^ - 5 ! = 2^5 e⁻² 120 = 32 e⁻² 120 = 4 e⁻² 15

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