on 12 A random variable has CDF given by ed d out of A i = 0, 1,2 F = 1 i=3 n if A = 0.11, then what is p3 ? Round your answer to two decimal places. Answer:n 14 In a new card game, you start by paying $57.27. From a well-shuffled full deck of cards draw 3 cards without replacement. If you draw 3 hearts, you win $207.72. If you draw 3 black cards, you win $422.82. For any other draws, d you win nothing. What is your expected winnings in this game? Round your answer to five decimal places. out of Answer:10 Given the following PDF i 22.9 24 72.5 98.9 12.3 ut of p_i 0.04 0.06 0.09 0.14 0.67 what is E[X]? Answer:n 16 The number of different mammal species observed along a transect through a forest is a random variable X with CDF 0.01, i = 0 d 0.16, i =1 out of 0.36, i = 7 Fi = 0.71, i = 12 0.96, i = 16 i = 23 What is the expected value of the random variable X? Round your answer to five decimal places. Answer:15 Large black-tailed gulls usually lay one to three eggs, and rarely have a fourth egg clutch. It is thought that clutch sizes are limited by how effectively parents can incubate their eggs. Suppose that on average, gulls have a 15.1% of laying 1 egg, 16.2% of laying 2 eggs, 27.1% chance of laying 3 eggs, and 41.6% chance of laying 4 eggs. What is the expected ed value of the number of eggs laid by a random sample of 100 gulls? Round your answer to five decimal places. Answer:18 A random variable has CDF given by A i = 0, 1, 2 F = 1 1 1=3 ut of if A = 0.56, then what is p2? Answer:estion 13 Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a yet spade, you win $74.35. For any club, you win $41.3 plus an extra $71.7 for the ace of clubs. What is the expected value wered of your winnings if you play the game? ked out of Round your answer to five decimal places. lag stion Answer:\fstion 11 A random variable has CDF given by let J A i = 0, 1, 2 vered Fi = 11 i=3 ed out of if A = 0.41, then what is po? g tion Answer:A probability density function for the random variable X is given by p; = k( )', where k is a constant. What value must 17 k be if X takes on integer values between 1 and n? Hint: Cl_jr = " if0