Question

Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X:

(a) f(x) = c(x² + 4), for x = 0, 1, 2, 3;

Answer 1

Given that,

$f(x) = c(x^2+4)$ $x=0,1,2,3$

We know,

$\sum_{x=0}^{3}f(x) = 1$

$c(4)+c(5)+c(8)+c(3) = 1$

$30c = 1$

Hence, $c = \dfrac{1}{30}$