You have two fair six-sided dice. The sides of each die are numbered from 1 to...

You have two fair six-sided dice. The sides of each die are numbered from 1 to 6. Suppose you roll each die once. Let ? be ???(??? 1,??? 2), and let ? be ???(??? 1,??? 2).
a) Find the joint PMF of ? and ?.
b) Find ???(?).
c) Find ?[?+?]

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6...

Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6 together. After rolling both dice, let X denote the number appearing on the foursided die and Y the number appearing on the six-sided die. Define W = X +Y . Assume X and Y are independent. (a) Find the moment generating function for W. (b) Use the moment generating function technique to find the expectation. (c) Use the moment generating function technique to find...

Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X...

Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X is the number appearing on the four-sided die and Y is the number appearing on the six-sided die. Define W=X+Y when they are rolled together. Assuming X and Y are independent, (a) find the moment generating function for W, (b) the expectation E(W), (c) and the variance Var(W). Use the moment generating function technique to find the expectation and variance.

Each of 3 fair dice has six sides numbered 1, 2, 3, 4, 5, and 6....

Each of 3 fair dice has six sides numbered 1, 2, 3, 4, 5, and 6. If these 3 dice are all rolled at the same time, what is the probability that exactly 2 of these dice will show a 1 ? Answers in word version please

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are...

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. a) Distinguish between the outcomes and events. b) What is the probability that both die roll ones? c) What is the probability that exactly one die rolls a one? d) What is the probability that neither die rolls a one? e) What is the expected number of ones? f) If you did this 1000 times, approximately...

Consider a six-sided fair dice. Complete the following tables for this die: Number on the dice...

Consider a six-sided fair dice. Complete the following tables for this die: Number on the dice Number of times it appears on the dice Relative frequency of seeing that number 1 2 3 4 5 6 Total This is the entire question, does not say how many times the dice is thrown

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...

You have two 5-sided fair dice. If you roll any individual die, the possible results are...

You have two 5-sided fair dice. If you roll any individual die, the possible results are 1, 2, 3, 4, or 5 each equally likely. Let A1 be the random result on the first die, and A2 be the random result on the second die. We define the random variable A = A1 + A2, the sum of values of two dice. Assume the signal X(t) = A for all times t. (a) Is A a discrete or a continuous...

A fair four sided die has two faes numbered 0 and two faces numbered 2. Another...

A fair four sided die has two faes numbered 0 and two faces numbered 2. Another fair four sided die has its faces numbered 0,1,4, and 5. The two dice are rolled. Let X and Y be the respective outcomes of the roll. Let W = X + Y. (a) Determine the pmf of W. (b) Draw a probability histogram of the pmf of W

Roll two fair dice. Each die has six faces. A. Let A be the event that...

Roll two fair dice. Each die has six faces. A. Let A be the event that either a 3 or 4 is rolled first followed by an odd number. P(A) = Round your answer to two decimal places. B. Let B be the event that the sum of the two dice is at most 7. P(B) = Round your answer to two decimal places. C. Are A and B mutually exclusive events? (Yes or No) D. Are A and B independent or...

You have 2 fair six-sided dice: one that is red and one that is blue. You...

You have 2 fair six-sided dice: one that is red and one that is blue. You conduct a random experiment by rolling the red die first and then rolling the blue die. Use this information and answer questions 2a to 2e. 2a) Determine whether following statements are outcome or event. You roll a red 1 and blue 3. You roll a red 2 and blue 5. The sum of two dice is greater than 9. 2b) How many outcomes are there...

Subjects