Select the random van'able that is discrete: Q The percentage increase or decrease in volume of an amount of liquid is assigned after that liquid is treated to a chemical reaction. 0 A number is assigned equal to the length of time a caller must wait on hold before they receive customer assistance from their bank. Q If a computer program takes longer than 10 seconds to compile, the value 1 is assigned. If it takes less than ll] seconds, the value 0 is assigned. 0 After 10 athletes throw a javelin, the longest distance thrown is recorded. Geoff is running a carnival game. He has 14 marbles in a bag: there are 4 green marbles, II" red marbles and 3 yellow marbles. To play a round ofthe game, a player randomly takes out a marble from the bag, notes the color and replaces it, \"dwen pulls a second marble from the bag and notes 'dwe color. So in effect, the player pulls 2 marbles from the bag. (However, the rst marble is put back in the bag and so potentially could be pulled twice.) Green marbles win 5 points, red marbles win 1 point and yellow marbles lose 2 points. Let X be the random variable that describes the number of points won by a player playing a single round of Geoff's marble game. Find the probability distribution for X. Give values for X as whole numbers and probabilities as decimal values to 3 decimal places. Enter the values for X in ascending order (lowest to highest) from left to right in the table. Suppose Y is a discrete random variable with probability distribution given by: P{Y=k)=k,'21,fork= 1,2,3,4,5,6 a) Calculate the expected value of Y. Give your answer to 2 decimal places. EWE b) Calculate the variance of Y. Give your answer as a decimal to 2 decimal places. mm = E