Question

In: Statistics and Probability

A fair die is rolled. If the result is greater than 4, a fair coin is...

A fair die is rolled. If the result is greater than 4, a fair coin is flipped, and otherwise, an unfair coin with P[H] = 2/3 is flipped. The outcome of the die roll is mapped to X, and the outcome of the coin flip is mapped to Y , with 1 for heads and −1 for tails.

(a) Find the joint PMF.

(b) Find both marginal PMFs. Do the marginal PMFs indicate independence?

Solutions

Expert Solution

thank you


Related Solutions

A fair coin is tossed, and a fair die is rolled. Let H be the event...
A fair coin is tossed, and a fair die is rolled. Let H be the event that the coin lands on heads, and let S be the event that the die lands on six. Find P(H or S).
If a fair coin is flipped twice and a standard 6 sided die is rolled once,...
If a fair coin is flipped twice and a standard 6 sided die is rolled once, what is the likelihood of getting two 'heads' on the coin and a '1' on the die? ​Express your answer as a percent rounded to the tenth place
A fair red die and a fair green die are rolled. (a) What is the probability...
A fair red die and a fair green die are rolled. (a) What is the probability that the sum of the numbers is even? (b) What is the probability that the number on the red die is more than the number on the green die? (c) What is the probability that the number on the red die is twice the number on the green die? (d) What is the probability that the number on the red die is different from...
Assume that a fair die is rolled. The sample space is , 1, 2, 3, 4,...
Assume that a fair die is rolled. The sample space is , 1, 2, 3, 4, 56 , and all the outcomes are equally likely. Find P Greater than 4 . Write your answer as a fraction or whole number. Assume that a fair die is rolled. The sample space is , 1, 2, 3, 4, 56 , and all the outcomes are equally likely. Find P Greater than 4 . Write your answer as a fraction or whole number.
A fair 4-sided die is rolled, let X denote the outcome. After that, if X =...
A fair 4-sided die is rolled, let X denote the outcome. After that, if X = x, then x fair coins are tossed, let Y denote the number of Tails observed. a) Find P( X >= 3 | Y = 0 ). b) Find E( X | Y = 2 ). “Hint”: Construct the joint probability distribution for ( X, Y ) first. Write it in the form of a rectangular array with x = 1, 2, 3, 4 and...
A die is rolled and, independently, a coin is tossed. Let X be the value of...
A die is rolled and, independently, a coin is tossed. Let X be the value of the die if the coin is H and minus the value of the die if the coin is T. (a) Calculate and plot the PMF of X. (b) Calculate E [X] and var(X) (c) Calculate and plot the PMF of X 2 − 2X. 2. A drunk walks down a street. Assume he starts at block 0. Every 10 minutes, he moves north a...
A) A coin is tossed and a die is rolled. Draw the tree diagram to list...
A) A coin is tossed and a die is rolled. Draw the tree diagram to list out every possible outcome for this sequence of events. How many total outcomes are possible? B) Elementary students are given an ID card that has a picture of their face followed by a 4 digit code. Assuming repetitions are allowed, how many ID cards are possible? C) Six balls are numbered: 1, 2, 3, 5, 8, and 13. A ball is selected, its number...
Example 4: A fair six-sided die is rolled six times. If the face numbered k is...
Example 4: A fair six-sided die is rolled six times. If the face numbered k is the outcome on roll k for k = 1, 2, 3, 4, 5, 6 we say that a match has occurred. The experiment is called a success if at least one match occurs during the six trials. Otherwise, the experiment is called a failure. The outcome space is O = {success, failure}. Let event A = {success}. Which value has P(A)? **This question has...
On each turn, bonnie is tossing a fair coin and Clyde is rolling a fair die....
On each turn, bonnie is tossing a fair coin and Clyde is rolling a fair die. They stop once Clyde rolls an odd number for the first time. Let X be the number of "Heads" that Bonnie's coin showed. a) Compute E[X] b) Compute var(X)
A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let...
A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let X denote the number of rolls required until the third 6 is rolled. Find the probability that fewer than 5 rolls will be required to roll a 6 three times.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT