A lottery has a grand prize jackpot worth 60 million dollars. The chance of winning from purchasing a single ticket is 1 in 23100000. the (a) What is the expected value of winning from a single ticket? (Round your answer to the nearest cent.) dollars #1 The expected value of winning is: (b) Would it be worth to buy a ticket for 2 dollars? Yes No Suppose you are playing a game. The random variable, Y, represents your net profit in dollars. The probability distribution of Y is as follows. (Round your answers to 4 decimal places, if needed.) #3 y P(Y=y) -3 -2 -1 3 0.1 0.23 ? 0.18 5 0.1 (a) What is the mean for net profit? (b) What is the median for net profit? (c) What is the standard deviation for net profit? A manufacturer produces items with a rectangular base. Let random variables denote the respective length (X) and width (Y) of the rectangle (in cm). Suppose X and Y are independent with the following parameter #5 values. E(X) = 4, Var(X) = 0.15, E(Y) = 10, Var(Y) = 0.35 The perimeter is then defined as 2X + 2Y. (Round your answers to 4 decimal places, if needed.) (a) What is the mean of the perimeter of the rectangle? (b) What is the standard deviation of the perimeter of the rectangle? You are given the following distributions, where some of the probabilities have been removed. Complete the tables so that each probability distribution is valid. (Round your answers to two decimal places.) #2 Distribution A Distribution B Distribution C x P(x) x P(x) x P(x) 1 5 0.2 3 0.75 2 0.75 10 4 0.2 15 0.2 5 20 0.4 Say you have a biased coin and you associate obtaining a head with the value 0 whereas obtaining a tail has a value of 2. Let X be the sum of the values obtained from tossing the coin three times. (Round your answers to 4 decimal places, if needed.) #4 (a) If the probability of getting heads in a single toss is 0.2, then what is the probability distribution of X? 0 P(X = x) (b) What is P(X