(a) If you roll a single die and count the number of dots on top, what...
4. Suppose that one die is rolled and you observe the number of dots facing up. The sample space for this experiment is S -(1, 2, 3, 4, 5, 6). The following table provides 5 different potential probability assignments to the possible outcomes Outcome Assignment AssignmentAssignment Assignment Assignment #1 0 16 #5 0.13 0.3 0.1 0.08 0.21 0.18 #2 #3 #4 16 4 4 16 4 0.5 16 6 0.5 a) which of the assignments #1-#5 are legitimate probability assignments?...
4. Suppose that one die is rolled and you observe the number of dots facing up. The sample space for this experiment is S -(1, 2, 3, 4, 5, 6). The following table provides 5 different potential probability assignments to the possible outcomes Outcome Assignment AssignmentAssignment Assignment Assignment #1 0 16 #5 0.13 0.3 0.1 0.08 0.21 0.18 #2 #3 #4 16 4 4 16 4 0.5 16 6 0.5 a) which of the assignments #1-#5 are legitimate probability assignments?...
4. Suppose that one die is rolled and you observe the number of dots facing up. The sample space for this experiment is S -(1, 2, 3, 4, 5, 6). The following table provides 5 different potential probability assignments to the possible outcomes Outcome Assignment AssignmentAssignment Assignment Assignment #1 0 16 #5 0.13 0.3 0.1 0.08 0.21 0.18 #2 #3 #4 16 4 4 16 4 0.5 16 6 0.5 a) which of the assignments #1-#5 are legitimate probability assignments?...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome is less...
52 68 Problem 6. (8 points) A six-sided die is loaded in a way that each odd number is twice as likely as each even number. All odd faces are equally likely, as are all even faces. (1) (5 points) Construct a probabilistic model for a single roll of this die; By constructing a probablistic model it means you should provide the sample space and the probabilities of all single events. (2) (3 points) Find the probability that the outcome...
7. Is the die fair? You suspect that a die has been changed so that the outcomes of a roll, the numbers 1 to 6, are not equally likely. You to the die 600 times and obtain the following result. Outcome Count 1 2 3 4 87 80 125 117 5 6 10091 - 1 - 1
Example 5.5. We roll a fair die then toss a coin the number of times shown on the die. What is the probability of the event A that all coin tosses result in heads? One could use the state space Ω = {(1, H), (1, T), (2, H, H), (2, T, T), (2, T, H), (2, H, T), . . . }. However, the outcomes are then not all equally likely. Instead, we continue the state space is Ω {1,...
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)...