Find the expected value of the random variable. Round to the nearest cent unless stated otherwise. Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value

Expected Value = - 0.5

Step-by-step explanation:

Expected Value [ E (X) ] = Σ {X. Probability (X) } = Σ [ (X). P (X) ]

Case 1 : Lottery Won

Probability = 1 / 1000

X Value = 500 - 1 = 499

Case 2 : Lottery Lost

Probability = 1 - Probability Winning = 999 / 1000

X Value = - 1

Expected Value:

(1 / 1000) (499) + (999 / 1000) (-1)

0.499 - 0.999

= - 0.5