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MHT CET202619 April 2026Morning ShiftMathematicsProbabilityActual

Given the probability density function (p.d.f.) of the random variable X, f(x) = 1 2a , 0 0 = 0 , otherwise, then which of the following is correct ?

Options

  1. AP (X a 2 )
  2. BP (X 3a 2 )
  3. CP (X P (X > 3a 2 )
  4. DP (X 3a 2 )

Correct answer

D. P (X 3a 2 )

Step-by-step solution

The given probability density function is f(x) = 1 2a for 0 We calculate the probability P (X P (X Next, we calculate the probability P (X > 3a 2 ) : P (X > 3a 2 ) = _ 3a 2 ^ 2a f(x) dx = _ 3a 2 ^ 2a 1 2a dx = 1 2a [x]_ 3a 2 ^ 2a = 1 2a (2a - 3a 2 ) = 1 2a ( a 2 ) = 1 4 Comparing the two probabilities, we get: P (X 3a 2 ) = 1 4 Answer: P (X 3a 2 )

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