- 1 of 3 ID: MST.FET.PD.DRV.01.0020A [1 mark] Select the random variable that is discrete: A number is assigned equal to the length of time a caller must wait on hold before they receive customer assistance from their bank. The percentage increase or decrease in volume of an amount of liquid is assigned after that liquid is treated to a chemical reaction. After 10 athletes throw a javelin, the longest distance thrown is recorded. O If a computer program takes longer than 10 seconds to compile, the value 1 is assigned. If it takes less than 10 seconds, the value 0 is assigned. 2 of 3 ID: MST.FET.PD.DRV.02.0030A [12 marks] Geoff is running a carnival game. He has 15 marbles in a bag: there are 4 green marbles, 7 red marbles and 4 yellow marbles. To play a round of the game, a player randomly takes out a marble from the bag, notes the color and replaces it, then pulls a second marble from the bag and notes the color. So in effect, the player pulls 2 marbles from the bag. (However, the first 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. X P(X = x) -3 of 3 ID: MST. FET.PD.DRV.03.0030A [2 marks] Suppose Y is a discrete random variable with probability distribution given by: P(Y - k) - k/10 - 3, for k - 31, 32, 33, 34 a) Calculate the expected value of Y. Give your answer to 2 decimal places. EM = b) Calculate the variance of Y. Give your answer as a decimal to 2 decimal places. VAR[Y] =