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AP EAMCET202124 Aug 2021Morning ShiftMathematicsProbabilityActual

If X is a poisson variate such that P(X=2)=P(X=3) , then e^3, P(X=4) is

Options

  1. A( 3 2 )^3
  2. B3 2
  3. Ce⁻³ 3^4 4 !
  4. De^3 3^4 4 !

Correct answer

A. ( 3 2 )^3

Step-by-step solution

X is poisson variate aligned & and P(X=2)=P(X=3) & e^ - ^2 2 ! = e^ - ^3 3 ! [ P(X=r)= e^ - ^r r ! ] & ^2 2 = ^3 6 6 2 = & =3 & P(X=4)= e^ - ^4 4 ! = e⁻³ (3)^4 4 ! & = e⁻³ 3 3 3 3 4 3 2 1 =e⁻³ ( 27 8 )=e⁻³ ( 3 2 )^3 & e^3 P(X=4)=e^3 e⁻³ ( 3 2 )^3 & = ( 3 2 )^3 & aligned

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