AP EAMCET201920 Apr 2019Morning ShiftMathematicsStatisticsActual
In a poisson distribution with unit mean, ( _ x=0 ^ |x- x | P(X=x)=( x ) is the mean of the distribution)
Options
- Ae
- B( 1 e )
- C( 2 e )
- D( 2 3 e )
Correct answer
C. ( 2 e )
Step-by-step solution
For the unit mean, ( x =1 ) ( aligned & so _ x=0 ^ |x- x | P(X=x)= _ x=0 ^ |x-1| e⁻¹ x ! & = 1 e [ 1 0 ! + _ x=1 ^ x-1 x ! ]= 1 e [1+ _ x=1 ^ 1 (x-1) ! - _ x=1 ^ 1 x ! ] aligned ) (= 1 e [1+e-(e-1)]= 1 e (1+e-e+1)= 2 e ) Hence, option (3) is correct.