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)
\(P(X = x)=\begin{cases}0.5; & \text{if } x_i=0\\ kx_i; & \text{if } x_i=1\\ k(4-x_i); & x_i=2 \text{ or } 3\\ 0; & \text{otherwise}\end{cases}\) Then the value of \(k\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(k=\displaystyle\frac{1}{8}\)
The probabilities of the values of X are
\( P(X = 0) = 0.5 \)
\( P(X = 1) = k \)
\( P(X = 2) = k(4 - 2) = 2k \)
\( P(X = 3) = k(4 - 3) = k \)
The probabilities add up to 1:
\( 0.5 + k + 2k + k = 1 \)
\( 4k = 0.5 \)
\( \displaystyle k = \frac{1}{8} \)
CBSE Applied Mathematics (Class XII):
Variance of Discrete Probability Distribution
