Question

In: Statistics and Probability

Sarah D's road manager plays a dice game with two dice. The six sides of on...

Sarah D's road manager plays a dice game with two dice. The six sides of on each die are numbered from 2 to 7. Define the random variable X to be the sum of the numbers on the up-face of the two dice when rolled.

a. Construct table showing PDF and the CDF of the random variable X

b. Calculate the mode of the distribution.

c. Calculate the expected value of X.

d. Calculate variance of X.

e. Calculate P(4

Expert Solution

a) The PDF of the random variable is constructed below.

X	4	5	6	7	8	9	10	11	12	13	14
P(X=x)	1/36	2/36	3/36	4/36	5/36	6/36	5/36	4/36	3/36	2/36	1/36

The CDF of the random variable is constructed below.

X	4	5	6	7	8	9	10	11	12	13	14
P(X<=x)	1/36	3/36	6/36	10/36	15/36	21/36	26/36	30/36	33/36	35/36	36/36=1

b) The mode of the distribution is the value of which has the largest probability of occurring. See the PDF table.

The mode is with probability 6/36 = 1/6.

c) The expected value is

d) The variance is calculated as

orchestra answered 1 year ago

A gambler plays a dice game where a pair of fair dice are rolled one time...

A gambler plays a dice game where a pair of fair dice are rolled one time and the sum is recorded. The gambler will continue to place $2 bets that the sum is 6, 7, 8, or 9 until she has won 7 of these bets. That is, each time the dice are rolled, she wins $2 if the sum is 6, 7, 8, or 9 and she loses $2 each time the sum is not 6, 7, 8, or...

For this problem, you will write a program in which the computer plays a dice game...

For this problem, you will write a program in which the computer plays a dice game called Craps. You might need to explore some Python documentation on random() for this homework assignment. PROVIDE A GRAPHICAL FLOWCHART as part of your submission for this solution Rules: The player rolls two six-sided dice. After rolling, the sum of what the dice show is calculated. If the sum is 7 or 11 on the first roll, the player wins. If the sum is...

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 ?[?+?]

In the game of craps, a player (known as the shooter) rolls two fair six-sided dice....

In the game of craps, a player (known as the shooter) rolls two fair six-sided dice. The shooter immediately loses if the sum of the dice is 2, 3, or 12 and immediately wins if the sum of the dice is 7 or 11 on the first roll. If the sum is anything else (4, 5, 6, 8, 9, or 10), that number becomes the point and the shooter rolls again. The shooter now wins by rolling that same point...

1. Write a program that plays a simple dice game between the computer and the user....

1. Write a program that plays a simple dice game between the computer and the user. When the program runs, it asks the user to input an even number in the interval [2..12], the number of plays. Display a prompt and read the input into a variable called ‘plays’ using input validation. Your code must ensure that the input always ends up being valid, i.e. even and in [2..12]. 2. A loop then repeats for ‘plays’ iterations. Do the following...

In a dice game a player first rolls two dice. If the two numbers are l...

In a dice game a player first rolls two dice. If the two numbers are l ≤ m then he wins if the third roll n has l≤n≤m. In words if he rolls a 5 and a 2, then he wins if the third roll is 2,3,4, or 5, while if he rolls two 4’s his only chance of winning is to roll another 4. What is the probability he wins?

Q3) Ahmed plays a game where he tosses two balanced 4 sided-dice, each with faces labeled...

Q3) Ahmed plays a game where he tosses two balanced 4 sided-dice, each with faces labeled by 1, 2, 3 and 4. He wins 2 points if the sum is 4. He wins 1 point if the sum is greater than 4. He loses k points if the sum is less than 4. i. Find the probability distribution sum. ii. Find the value of k which achieves the fairness of game. (i.e. The fairness is achieved if the game is...

PYTHON GAME OF PIG The game of Pig is a simple two player dice game in...

PYTHON GAME OF PIG The game of Pig is a simple two player dice game in which the first player to reach 100 or more points wins. Players take turns. On each turn a player rolls a six-sided die. After each roll: a) If the player rolls a 1 then the player gets no new points and it becomes the other player’s turn. b) If the player rolls 2-6 then they can either roll again or hold. If the player...

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.

. Three Dice of a Kind Consider the following game: You roll six 6-sided dice d1,…,d6...

. Three Dice of a Kind Consider the following game: You roll six 6-sided dice d1,…,d6 and you win if some number appears 3 or more times. For example, if you roll: (3,3,5,4,6,6) then you lose. If you roll (4,1,3,6,4,4) then you win. What is the probability that you win this game?