How to come up with a probability distribution knowing the mean value?

Expected Value for a probability distribution?

• I don't normally come here for homework help, but I'm stuck! Trying to find the expected value of this probability distribution: bonus points | -20 | 0 | 1 | 5 | 10 probability | .25|.15|.35|.15|.1 can someone give me a push in the right direction? i tried googling help, but the answers weren't what i was looking for :/

• Answer:

  Dear candykitty114, For convenience, let B have the probability distribution of your table. Then the mean, or expected value of B is a probability-weighted sum of the respective values that B can attain (or phrased another way, the expected value is a weighted average of the possible values, where the probabilities are the weights). E[B] = Σ p[i] b[i], for all i in {1, 2, 3, 4, 5} = p[1] b[1] + p[2] b[2] + p[3] b[3] + p[4] b[4] + p[5] b[5] = (0.25)(-20) + (0.15)(0) + (0.35)(1) + (0.15)(5) + (0.10)(10) = -5.00 + 0.00 + 0.35 + 0.75 + 1.00 = -2.90 [← this is the answer]. In case you are unfamiliar with the notation, E[B] means the "expectation of B" (or "expected value of B"); Σ is the summation symbol, where the expression to its right is summed for all values of i from 1 to 5; p[i] is the i-th probability from the distribution; and b[i] is the i-th "bonus points" value from the distribution. Also, although not universally followed, it's fairly common practice for the individual values from a distribution to be denoted with lowercase letters (such as b), which helps to distinguish them from random variables in uppercase representing the entire table (such as B).