Find the expected value of each random variable. а) х 15 30 45 P(X = x) 0.4 0.1 0.5 b) x P(X=x) 1 7 0.3 0.4 0.1 0.2 a) The expected value is (Type an integer or a decimal. Do not round.)

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is hth, then =Rhth2. Suppose that the random variable X is defined in terms of R as follows: =X−2R1. The values of X are given in the table below.   Outcome tth thh hht htt ttt hhh hth tht Value of  X 1 3 3 1 −1 5 3 1   Calculate the values of the probability distribution function of X, i.e. the function pX. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value  x  of  X         pXx

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Suppose that X is a N(3,4) random variable and suppose that Y=5X+2. Determine P(Y>18.5).