The probability distribution of a random variable X is given by x 0 1 2 3 4 P(x) 0.4 0.3 0.1 0.1 0.1 Then…

The variance of a random variable is given by $\text{Var}(X) = E(X^2) - [E(X)]^2$.

The expected value $E(X)$ is computed as:

$E(X) = (0)(0.4) + (1)(0.3) + (2)(0.1) + (3)(0.1) + (4)(0.1) = 1.2$

Similarly, the expected value of $X^2$ is:

$E(X^2) = (0^2)(0.4) + (1^2)(0.3) + (2^2)(0.1) + (3^2)(0.1) + (4^2)(0.1) = 3.2$

Therefore, the variance is:

$\text{Var}(X) = 3.2 - (1.2)^2 = 1.76$

Final answer: A