Question

Let $f_1(x)$ be the probability density function of the $N(0,1)$ distribution, and $f_2(x)$ be the probability density function of the $N(0, 6)$ distribution. Let $Y$ be a random variable with probability density function
$f(x) = 0.6 f_1(x) + 0.4 f_2(x), \quad -\infty < x < \infty.$
Then $\text{Var}(Y)$ is equal to:

• A. 7
• B. 3
• C. 3.5
• D. 1

Answer 1

Answer: (B)

3

Answer 2

The correct option is (B): 3