Question

The probability distribution of a random variable X is given by\[ \begin{array}{|l|c|c|c|c|c|} \hline \mathrm{X}=x_i & 0 & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}\left(\mathrm{X}=x_i\right) & 0.4 & 0.3 & 0.1 & 0.1 & 0.1 \\ \hline \end{array} \]

Then the variance of X is

• A. 1.76
• B. 2.45
• C. 3.2
• D. 4.8

Hint:

Use variance = E(X squared) minus the square of the mean.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
For a random variable, \(\text{Var}(X)=E(X^2)-[E(X)]^2\).

Step 2: Mean
\(E(X)=0(0.4)+1(0.3)+2(0.1)+3(0.1)+4(0.1)=0.3+0.2+0.3+0.4=1.2\)

Step 3: Mean of squares
\(E(X^2)=0+1(0.3)+4(0.1)+9(0.1)+16(0.1)=0.3+0.4+0.9+1.6=3.2\)

Step 4: Calculation
\(\text{Var}(X)=3.2-(1.2)^2=3.2-1.44=1.76\).
This matches option (A).

Final Answer:
The variance of X is 1.76. \[ \boxed{\text{(A) }1.76} \]