![SectionA Q1. a. Two dice are rolled repeatedly until their scores, Χ, and X, differ by at least two. Find: (i) The probabilities of all possible values of the sum of the scores X, + X2. (i) The marginal probability of all values of X. b. Adice is rolled repeatedly until the total score of all the rolls is at least six. This takes K rolls. Find (i) The probabilities of all possible values of K. (i) The expected value E[K] and variance, E[K2]- E[K]2 (iii) The conditional probabilities of K given the first roll was less than three. c. A model of oil prices is tested on historical data. When the model predicted the price would exceed $100 per barrel, this actually occured with probability 80%. Cor- respondingly if the prediction was the price will stay below $100 per barrel, there was a 40% chance the model is wrong. There is a 20% chance the price of oil will exceed $100 per barrel next year. If the model predicts this will happen, what is the probability it will occur in practice?](http://img.homeworklib.com/questions/bf8762e0-c5d3-11ea-a4a1-bd60db462b92.png?x-oss-process=image/resize,w_560)
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SectionA Q1. a. Two dice are rolled repeatedly until their scores, Χ, and X, differ by...
Two dice are rolled repeatedly until the sum of the two numbers rolled is 10 or...
Two dice are rolled repeatedly until the sum of the two numbers rolled is 10 or more. a) What is the probability that exactly 5 rolls are needed? (Count each time you roll the dice as one roll). b) What is the probability that more than 5 rolls are needed? c) Find the expected number of rolls.
A tetrahedron (four-sided die) is rolled twice and the sum X of k is the results...
A tetrahedron (four-sided die) is rolled twice and the sum X of k is the results of the two rolls is recorded. We know that the chance that X proportional to k. (a) What is the probability model for X, i.e., uhat values can X take, and what are the corresponding probabilities? (b) Compute the chance that the sum of the two rolls will erceed but ill not be more than b (c) Compute the erpected value of x.
Problem 2. A tetrahedron four-sided die) is rolled turice and the sum X of the results...
Problem 2. A tetrahedron four-sided die) is rolled turice and the sum X of the results of the two rolls is recorded. We know that the chance that X-k is proportional to k. (a) What is the probability model for X, i.e., what values can X take, and what are the corresponding probabilities? (b) Compute the chance that the sum of the two rolls wieceed but will not be more than 6. (c) Compute the expected value of X
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil-...
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil- ity of rolling the value i is Pi, i = 1, … ,6. Let Xn denote the number of distinct values that appear in n rolls. (a) Find E|X, and E21 (b) What is the probability that in the n rolls of the dice, for n 2 3, a 1, 2, and 3 are each rolled at least once?
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the...
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the number left over after this repeated subtraction. The number Y is almost the same as the remainder left over after dividing N into X equal parts, ercept that Y will equal X, not 0, if N is evenly divisible...
I'm very confused about how to do it. I think you have to use R to...
I'm very confused about how to do it. I think you have to use R
to solve the question. Any help would be appreciated thanks.
Suppose you work for a casino and have been tasked with determining whether a particular six-sided die is fair, in which case the probability is exactly 1/6 that a roll of the die results in any one of its six face values. Suppose there are two commonly used sets of face value weights among biased...
2. Let's now use Excel to simulate rolling two 6-sided dice and finding the minimum of...
2. Let's now use Excel to simulate rolling two 6-sided dice and finding the minimum of both dice. • Create a new Excel sheet in your document. Click on cell Al, then click on the function icon f. and select Math&Trig, then select RANDBETWEEN. In the dialog box, enter 1 for bottom and enter 6 for top. • After getting the random number in the first cell, click and hold down the mouse button to drag the lower right corner...
please provide formulas i need Problem 4: Estimates A company purchases Olive oil according to this...
please provide formulas i need
Problem 4: Estimates A company purchases Olive oil according to this price schedule. • • For the first 1000 Litres, $7.10 per litre For any of the next 3000 Litres 56.60 per litre For any oil beyond 4,000 Litres, 55 80 per litre The Purchase Estimate spreadsheet calculates the total price of buying x litres of oil, wherexia number input to a cell (Ordered) on the worksheet with values that may fall into any or...
Assignment Specifications We are going to use the Monte Carlo Method to determine the probability of...
Assignment Specifications We are going to use the Monte Carlo Method to determine the probability of scoring outcomes of a single turn in a game called Pig. Your Task For this assignment you will simulate a given number of hold?at?N turns of a game called Pig, and report the estimated probabilities of the possible scoring outcomes. You are NOT implementing the game of Pig, only a single turn of this game. The value of N will be acquired via user...
Part E - Area Under the Curve (possible 12 points) 2 Activity: In the field of statistics the fun...
i
have no idea how to do this please help
Part E - Area Under the Curve (possible 12 points) 2 Activity: In the field of statistics the function fx)e 2 is used to model data like birth weight or height. In Lesson 8, you learned how to calculate z-scores, which then those scores related to the Project 2 345 MTHH 04 number of standard deviations that specific value was from the mean. Now, you will extend that knowledge of...
A tetrahedron (four-sided die) is rolled twice and the sum X of k is the results of the two rolls is recorded. We know that the chance that X proportional to k. (a) What is the probability model for X, i.e., uhat values can X take, and what are the corresponding probabilities? (b) Compute the chance that the sum of the two rolls will erceed but ill not be more than b (c) Compute the erpected value of x.
Problem 2. A tetrahedron four-sided die) is rolled turice and the sum X of the results of the two rolls is recorded. We know that the chance that X-k is proportional to k. (a) What is the probability model for X, i.e., what values can X take, and what are the corresponding probabilities? (b) Compute the chance that the sum of the two rolls wieceed but will not be more than 6. (c) Compute the expected value of X
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil- ity of rolling the value i is Pi, i = 1, … ,6. Let Xn denote the number of distinct values that appear in n rolls. (a) Find E|X, and E21 (b) What is the probability that in the n rolls of the dice, for n 2 3, a 1, 2, and 3 are each rolled at least once?
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the number left over after this repeated subtraction. The number Y is almost the same as the remainder left over after dividing N into X equal parts, ercept that Y will equal X, not 0, if N is evenly divisible...
I'm very confused about how to do it. I think you have to use R
to solve the question. Any help would be appreciated thanks.
Suppose you work for a casino and have been tasked with determining whether a particular six-sided die is fair, in which case the probability is exactly 1/6 that a roll of the die results in any one of its six face values. Suppose there are two commonly used sets of face value weights among biased...
2. Let's now use Excel to simulate rolling two 6-sided dice and finding the minimum of both dice. • Create a new Excel sheet in your document. Click on cell Al, then click on the function icon f. and select Math&Trig, then select RANDBETWEEN. In the dialog box, enter 1 for bottom and enter 6 for top. • After getting the random number in the first cell, click and hold down the mouse button to drag the lower right corner...
please provide formulas i need
Problem 4: Estimates A company purchases Olive oil according to this price schedule. • • For the first 1000 Litres, $7.10 per litre For any of the next 3000 Litres 56.60 per litre For any oil beyond 4,000 Litres, 55 80 per litre The Purchase Estimate spreadsheet calculates the total price of buying x litres of oil, wherexia number input to a cell (Ordered) on the worksheet with values that may fall into any or...
i
have no idea how to do this please help
Part E - Area Under the Curve (possible 12 points) 2 Activity: In the field of statistics the function fx)e 2 is used to model data like birth weight or height. In Lesson 8, you learned how to calculate z-scores, which then those scores related to the Project 2 345 MTHH 04 number of standard deviations that specific value was from the mean. Now, you will extend that knowledge of...
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