Take a simple experiment of rolling a pair of balanced dice. Each die has six sides,...

Take a simple experiment of rolling a pair of balanced dice. Each die has six sides, each side contains one to six spots. Let us define the random variable x to be the sum of the spots on the two dice. Display the probability mass function and the distribution function for the random variable x.

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milcah answered 6 months ago

An experiment consists of rolling three fair dice --- a red die, a blue die, and...

An experiment consists of rolling three fair dice --- a red die, a blue die, and a white die --- and recording the number rolled on each die. Assume that the dice are fair, so that all outcomes are equally likely. (1) What probability should be assigned to each outcome? equation editorEquation Editor (2) What is the probability that the sum of the numbers rolled is 5? equation editorEquation Editor (3) What is the probability that the sum of the...

for the experiment of rolling an ordinary pair of dice, find the probability that the sum...

for the experiment of rolling an ordinary pair of dice, find the probability that the sum will be even or a multiple of 6. ( you may want to use a table showing the sum for each of the 36 equally likely outcomes.)

An experiment consists of rolling six-sided dice twice. &

An experiment consists of rolling six-sided dice twice. (10) List the sample space for this experiment. Find the probability distribution for this experiment where x represents the number of even numbers in the 2 rolls. Find the mean of the probability distribution. Find the standard deviation of the probability distribution. Would it be unusual to get 2 even numbers? Why or why not? (show your work)

7. [10 marks] Consider an experiment of rolling two regular (or fair) balanced six-sided dice. a)...

7. [10 marks] Consider an experiment of rolling two regular (or fair) balanced six-sided dice. a) List out all the possible outcomes. b) Define X as the amount you will win in the following game. You will win $100 when a double (two identical numbers) is rolled; you will win $10 when an odd sum is rolled; and you will win $30 when other even sum is rolled, excluding doubles. Define X as the amount you will win in this...

You are rolling a pair of balanced dice in a board game. Rolls are independent. You...

You are rolling a pair of balanced dice in a board game. Rolls are independent. You land in a danger zone that requires you to roll doubles (both faces show the same number of spots) before you are allowed to play again. 1. What is the probability of rolling doubles on a single toss of the dice? A) 25/36 B) 5/36 C) 1/6 D) 1/36 2. What is the probability that you do not roll doubles on the first toss,...

1. In the experiment of rolling a balanced die twice. Let X be the minimum of...

1. In the experiment of rolling a balanced die twice. Let X be the minimum of the two numbers obtained and Y be value of the first roll minus the value of the second roll. Determine the probability mass functions and cumulative distribution functions of X and Y, and sketch their graphs please also solve probability for Y

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 ?[?+?]

A balanced die with six sides is rolled 60 times. For the binomial distubtion of X...

A balanced die with six sides is rolled 60 times. For the binomial distubtion of X = Numbers of 6’s, what is n, what is p, and what is q Find the mean and standard deviation of the distribution of X. What do these values tell you? If you observe X = 2, would you be skeptical that the die is balanced? Explained why, based on the mean and standard deviation of . How long would the value of X...

The experiment of rolling a fair six-sided die twice and looking at the values of the...

The experiment of rolling a fair six-sided die twice and looking at the values of the faces that are facing up, has the following sample space. For example, the result (1,2) implies that the face that is up from the first die shows the value 1 and the value of the face that is up from the second die is 2. sample space of tossing 2 die A pair of dice is thrown. Let X = the number of multiples...

Consider four nonstandard dice, whose sides are labeled as follows (the 6 sides on each die...

Consider four nonstandard dice, whose sides are labeled as follows (the 6 sides on each die are equally likely). A: 4, 4, 4, 4, 0, 0 B: 3, 3, 3, 3, 3, 3 C: 6, 6, 2, 2, 2, 2 D: 5, 5, 5, 1, 1, 1 These four dice are each rolled once. Let A be the result for die A, B be the result for die B, etc. (a) Find P(A > B), P(B > C), P(C >D),...

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