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MHT CET202312 May 2023Morning ShiftMathematicsProbabilityActual

The p.m.f of random variate X is P ( X )= cases 2 x n ( n +1) , & x=1,2,3, , n 0, & otherwise cases Then E(X)=

Options

  1. An +1 3
  2. B2 n +1 3
  3. Cn +2 3
  4. D2 n -1 3

Correct answer

B. 2 n +1 3

Step-by-step solution

aligned P ( X ) & = array l 2 x n ( n +1) , x=1,2,3, , n 0, othewise array . E ( X ) & = _ i =1 ^ n x_ i p (x_ i ) & = 2 n ( n +1) + 8 n ( n +1) + + 2 n ^2 n ( n +1) & = 2 (1^2+2^2+ + n ^2 ) n ( n +1) & = 2 n ( n +1)(2 n +1) 6 n ( n +1) & = 2 n +1 3 aligned

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