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MHT CET202012 Oct 2020Morning ShiftMathematicsContinuity and DifferentiabilityActual

Which of the following functions is not p.d.f. of a continuous random variable X?

Options

  1. AF₃
  2. BF₄
  3. CF₁
  4. DF₂

Correct answer

B. F₄

Step-by-step solution

Since P(X=1)=P(X=2)= =P(X=n) and P(X=1)+P(X=2)+ +P(X=n)=1 , We get P(X=1)=P(X=2)=P(X=n)= 1 n array |c|c|c|c| x _ i & p _ i & x _ i p _ i & x _ i ² p _ i 1 & 1 n & 1 n & 1 n 2 & 1 n & 2 n & 2² n 3 & 1 n & 3 n & 3² n & & & n & 1 n & n n & n ² n array x _ i p _ i = 1 n + 2 n + 3 n + + n n = 1 n (1+2+3+ n )= 1 n n ( n +1) 2 = n +1 2 aligned x₁ ² p₁ &= 1² n + 2² n + 3² n + + n² n &= 1 n (1²+2²+3²+ +n² )= 1 n n(n+1)(2 n+1) 6 - (n+1)(2 n+1) 6 aligned Given E(X)=V(X) array l x_ i p_ i = x_ i ² p_ i - [ x_ i p_ i ]² n+1 2 =

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