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AP EAMCET202319 May 2023Morning ShiftMathematicsProbabilityActual

If X is random variable with probability distribution P(X=k)= (k+1) c 2^k , k=0,1,2, , then P(X 3)=

Options

  1. A1 4
  2. B5 16
  3. C5 11
  4. D3 16

Correct answer

B. 5 16

Step-by-step solution

gathered P(X=k)= (k+1) C 2^k , k=0,1,2, . P(X= k )= C (1+ 2 2 + 3 2^2 + 4 2^3 + ) 1=C (1+ 2 2 + 3 2^2 + 4 2^3 + ) 1 2 =C ( 1 2 + 2 2^2 + 3 2^3 + 4 2^4 + ) - - - - - 1 2 =C (1+ 1 2 + 1 2^2 + 1 2^3 ) C= 1 4 gathered Now, P(X 3)=1-[P(X=0)+P(X=1)+P(X=2)] =1- [C+ 2 C 2 + 3 C 4 ]=1- 11 C 4 =1- 11 16 = 5 16

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