A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75, $50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?

Question

A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75, $50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?

Answer 1

The expected value of x is the sum of each probability of a payoff times the payoff. In formal terms:

E(x) = summation of the x_iP(x_i) for P(x_i) being the discrete probability distribution of the x_i

In this case (.75)($10) + .25($50)