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Mean (expected value) of a discrete random variable

AP.STATS: VAR‑5 (EU), VAR‑5.C (LO), VAR‑5.C.1 (EK), VAR‑5.C.2 (EK), VAR‑5.D (LO), VAR‑5.D.1 (EK) CCSS.Math: HSS.MD.A.2
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A construction company is considering submitting bids for two contracts. It will cost the company dollar sign, 10, comma, 000 to prepare and submit the bids, and if won, each bid would produce dollar sign, 50, comma, 000 of income to the company. The company estimates that it has a 10, percent chance of winning any given bid.
Here is the probability distribution of X, equals the number of bids the company wins, and M, equals the amount of money the company profits from the bids.
X, equals, \#, start text, space, o, f, space, b, i, d, s, space, w, o, n, end text012
M, equals, start text, p, r, o, f, i, t, end textminus, dollar sign, 10, comma, 000dollar sign, 40, comma, 000dollar sign, 90, comma, 000
Probability0, point, 810, point, 180, point, 01
Calculate the mean of M.
mu, start subscript, M, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text