Question

For the given dataset:
\[ \begin{array}{c|ccc} x & 2 & 3 & 4\\ \hline f(x) & \frac14 & \frac12 & \frac14 \end{array} \] Which of the following is the expected value of \(x\)?

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. \(4\)

Hint:

For discrete probability distribution, expected value is found by multiplying each value of \(x\) with its probability and then adding all products.

Answer 1

The Correct Option is C

Concept:
For a discrete probability distribution, the expected value or mean is: \[ E(X)=\sum xP(x) \]

Step 1: Write the given values. \[ x=2,3,4 \] and \[ P(2)=\frac14,\quad P(3)=\frac12,\quad P(4)=\frac14 \]

Step 2: Apply the expected value formula. \[ E(X)=2\left(\frac14\right)+3\left(\frac12\right)+4\left(\frac14\right) \] \[ E(X)=\frac{2}{4}+\frac{3}{2}+\frac{4}{4} \] \[ E(X)=\frac12+\frac32+1 \] \[ E(X)=2+1 \] \[ E(X)=3 \] \[ \therefore \text{Correct Answer is (C)} \]