Question

6. Define or state the expected value of a discrete random variable X (E(x) is given as____).

Answer 1

By definition, a random variable X is called discrete, if it can take only countable number of values. Suppose that X takes values $x_i$ with probabilities $p_i$, $\sum_{i=1}^{+\infty}p_i=1$ . Then its expected value is (see e.g., https://en.wikipedia.org/wiki/Expected_value) $E[X]=\sum_{i=1}^{+\infty}x_ip_i$ .