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MHT CET202310 May 2023Morning ShiftMathematicsProbabilityActual

For a binomial variate X with n=6 if P(X=4)= 135 2¹² , then its variance is

Options

  1. A8 9
  2. B1 4
  3. C4
  4. D9 8

Correct answer

D. 9 8

Step-by-step solution

aligned & Given, P(X=4)= 135 2¹² & ^6 C₄ p^4 q^2= 135 2¹² & 15 p^4 q^2= 135 2¹² & p^4 q^2= 3^2 2¹² & p^2 q= 3 2^6 & p^2(1-p)= 3 64 & p^2(1-p)= ( 1 4 )^2 (1- 1 4 ) & p= 1 4 & and q=1- 1 4 = 3 4 & Variance =n p q & =6 1 4 3 4 & = 9 8 aligned

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