For a discrete random variable X, which of the following computes the expected value?
A) $\sum f\left(x_{i}\right)$

B) $\sum_{i=1}^{\infty} x_{i} f\left(x_{i}\right)$

C) $\sum_{i=1}^{\infty} x_{i}$

D) $\sum \frac { f ( x ) } { x }$

Question

For a discrete random variable X, which of the following computes the expected value?
A) $\sum f\left(x_{i}\right)$

B) $\sum_{i=1}^{\infty} x_{i} f\left(x_{i}\right)$

C) $\sum_{i=1}^{\infty} x_{i}$

D) $\sum \frac { f ( x ) } { x }$

Quizplus · Accepted Answer

The definition of expected value for a discrete random variable X is given by E(X) = ∑x_if(x_i), where x_i is a possible value of X and f(x_i) is the probability of X taking the value x_i. Therefore, option B is the correct formula to compute the expected value of X, as it follows this definition. Options A and C are incorrect, as they do not take into account the probability of each possible value. Option D is also incorrect, as it involves dividing by X, which may not always be defined for all possible values of X.

For a Discrete Random Variable X, Which of the Following ∑f(xi)\sum f\left(x_{i}\right)∑f(xi​)

For a Discrete Random Variable X, Which of the Following $\sum f\left(x_{i}\right)$