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MHT CET202013 Oct 2020Evening ShiftMathematicsProbabilityActual

If and a² are mean and variance of a random variable X whose p. m . f . is given by P(X=x)= ( array l 6 x array ) ( 1 x )^ x ( 2 x )^ 6-x , x=0,1,2,3, 6 , then the value of 2 +12 ²=

Options

  1. A4
  2. B8
  3. C20
  4. D16

Correct answer

C. 20

Step-by-step solution

We have P(X=x)= 6 x ( 1 3 )³ ( 2 3 )^ 6-x = ( 1 3 + 2 3 )⁶ Thus, n =6, p = 1 3 and q = 2 3 Mean = np =(6) ( 1 3 )=2 and variance =(6) ( 1 3 ) ( 2 3 )= 4 3 2 +12 ²=2(2)+12 ( 4 3 )=4+16=20

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