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AP EAMCET202125 Aug 2021Evening ShiftMathematicsProbabilityActual

For a binomial distribution with mean 6 and variance 2. Then, the value of P(X = 8) is

Options

  1. A2^8 3^8
  2. B2^8 3^7
  3. C2^8 3^9
  4. D2 3^7

Correct answer

B. 2^8 3^7

Step-by-step solution

Given Mean = np = 6 … (i) Variance = npq = 2 where q = 1 − p … (ii) 6 q=2 using Eq. (i) in Eq. (ii) aligned q & =1 / 3 p & =1-1 / 3=2 / 3 aligned From Eq. (i), we get aligned n & = 6 p = 6 2 / 3 =9 P(X=8) & = ^n C_r(q)^ n-r (p)^r & = ^9 C₈ ( 1 3 )⁹⁻⁸ ( 2 3 )^8 & =9 1 3 ( 2 3 )^8= 2^8 3^7 aligned

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