(1 point) You are to roll a fair die n = 104 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i = 1,2, ..., 104 (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll...
You are to roll a fair die n=123 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i=1,2,⋯,123. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die. μXi= (at least one decimal)...
In a dice game, you roll a fair die three times, independently. If you don’t roll any sixes, you lose 1 dollar. If you roll a six exactly once, you win one dollar. If you roll a six exactly twice, you win two dollars. If you roll a six all three times, you win k dollars. (A) Let k = 3. What is the expected value of the amount you would win by playing this game (rounded to the nearest...
1. A casino wants to see if a six-sided die is fair. They perform an experiment in which they roll the die 100 times and count the number of times the result is a 3. (a) Is this a one or two-sided test? Explain your answer in a complete sentence. (b) Set up the hypotheses for this test both in words and in terms the parameter p which denotes the theoretical probability for getting a roll of the die giving...
Question 3 3 pts Matching problem [Choose] You roll a fair six-sided die 500 times and observe a 3 on 90 of the 500 rolls. You estimate the probability of rolling a 3 to be 0.18 Choose) You roll a fair six-sided die 10 times and observe a 3 on all 10 rolls. You bet the probability of rolling a 3 on the next rollis close to O since you have already had 10 3's in a row You assign...
You roll a fair six-sided die 5 times. What is the probability that EXACTLY one of the rolls lands on 1 (round your answer to 2 decimal places)? 10 4/8
You roll a 6-sided die. The die has one to six spots on each side, with each count (1, 2, 3, 4, 5, or 6) appearing once. The die is fair: each side has an equal chance that it will be up when the die lands. What is the probability that you will roll a value greater than or equal to 2? Express your answer in decimal form to 3 decimal places.
Suppose you are going to roll a die 60 times and record the proportion of times that a 1 or 2 is showing, s. The sampling distribution of s should be centered about....?
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let N be the number of times the two dice have to be rolled before the game is decided. (d) Assume that you get paid $10 for winning in the first round, $1 for winning in any other round, and nothing otherwise. Compute your expected winnings. Answer: (d) You get paid $10 with...
Question 4: You roll a fair die once. Define the events A = “the result is one of the numbers 1, 3, and 4”, B = “the result is one of the numbers 3, 4, 5, and 6”. • Are the events A and B independent? Jusitfy your answer using the definition of independence. • Are the events A and B independent? Jusitfy your answer using the definition of conditional probability. Question 4: You roll a fair die once. Define...