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 hhh, then R (hhh)=3. Suppose that the random variable X is defined in terms of R as follows: X= 2R-2R^2-3. The values of X are given in the table below.

Consider the following random experiment: we toss a two-sided coin (H on one side and T on the other side) n = 3616 times. In any given toss, the probability the coin comes up H is p = P(H) = 0.3. Each time the coin comes up H we give Tom 2 dollars and each time the coin comes up T we take from Tom 1 dollar (so Tom either gets 2 or gets -1, i.e., loses 1 dollar). How many dollars do we expect Tom will get on "average", i.e., per experiment?

q13- X and Y are two independent random variables. We know V(X) = 26.43 and V(Y) = 23.67, then V(8X + 5Y) is: a. 862.68 b. 2283.27 c. 329.79 d. 16490.91

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 tth, then =Rtth1. Suppose that the random variable X is defined in terms of R as follows: =X−R2−3R4. The values of X are given in the table below.   Outcome htt tht hth thh ttt hhh hht tth Value of  X −6 −6 −6 −6 −4 −4 −6 −6   Calculate the values of the probability distribution function of X, i.e. the function p X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.