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Let X denote the number of hours a student studies on a selected day. The probability distribution of X is given by (where k is some unknown…

CUET UG 2025 — Mathematics Algebra

2025mcqmedium

Let X denote the number of hours a student studies on a selected day. The probability distribution of X is given by (where k is some unknown constant)

P(X=xi)={0.5,if xi=0,kxi,if xi=1,k(4−xi),if xi=2 or 3,0,otherwise.P(X = x_i) = \begin{cases} 0.5, & \text{if } x_i = 0, \\ kx_i, & \text{if } x_i = 1, \\ k(4 - x_i), & \text{if } x_i = 2 \text{ or } 3, \\ 0, & \text{otherwise}. \end{cases}P(X=xi​)=⎩⎨⎧​0.5,kxi​,k(4−xi​),0,​if xi​=0,if xi​=1,if xi​=2 or 3,otherwise.​

Then the value of k is

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

  1. A

    k=14k = \frac{1}{4}k=41​

  2. B

    k=13k = \frac{1}{3}k=31​

  3. C

    k=18k = \frac{1}{8}k=81​

  4. D

    k=12k = \frac{1}{2}k=21​

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