Mathematics · Probability Distributions

Let X1 and X2 be two independent random variables such that X1 follows a gamma distribution with mean 10 and variance 10, and X2 ~ N(3, 4). Let f1 and f2 denote the probability density functions of X1 and X2, respectively. Define a new random variable Y whose density function for y ∈ ℜ is given by f(y) = 0.4 f1(y) + q f2(y). Which of the following statements is true?