1. a. Two fair dice are rolled at once. Let X denote the difference in the number of dots that appearon the top faces of the two dice (positive differences only). Thus, for example if a one and a fiveare rolled, X = 4, and if two sixes are rolled, X = 0. Calculate and graph the probability distribution.Xb. Calculate the Expected Value. 2.The die is rolled five times.a. Find the probability of three 6's occurring.b. Find the probability of at least one 6 being rolled.

Given : Two dice have been thrown X denote the difference between the dots shows in the top of two…

Answered: 1. a. Two fair dice are rolled at once.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You roll five fair six-sided dice. Let X denote the sum of the numbers shown. Compute the expectation and the variance of X.
A family has three children. If the genders of these children are listed in the order they are born, there are eight possible outcomes: BBB, BBG, BGB, BGG, GBB, GBG, GGB, and GGG. Assume these outcomes are equally likely. Let X represent the number of children that are girls. Find the probability distribution of X.
Which of the following is true about a probability distribution? O a. The outcomes do not need to be mutually exclusive. O b. The probability of each outcome must be between 0 and 1, inclusive. O c. The representation must be graphed, not tabular or algebraic. O d. The sum of all possible outcomes must not equal 1.
A die is weighted in such a way that each of 2, 4, and 6 is three times as likely to come up as each of 1, 3, and 5. Find the probability distribution. Outcome 1 2 3 4 5 6 Probability What is the probability of rolling less than 5?
QUESTION 2 a) Based on the past data, 8% of customers will order a dessert with the meal at a noodle's restaurant. 14% of them will order a bottled beverage. i. What is the probability that a customer will order both a dessert and a bottled average? (2 marks) ii. The customers have ordered a dessert with the meal. Calculate the probability that he or she will order a bottled beverage. (2 marks) b) The Graduate Management Admission Test (GMAT) is a requirement for all applicants of MBA programs. A variety of preparatory courses are designed to help applicants improve their GMAT scores, which range from 200 to 800. Suppose that a survey of MBA students reveals that among GMAT scorers at least 650, 72% took a preparatory course; whereas among GMAT scores of less than 650 only 31% took a preparatory course. The probability for an applicant to score at least 650 is 30%. Suppose he was not taking the preparatory course. What is his probability of achieving 650 or more for GMAT score? (5…
1. Use this table for the following questions: Female Male TotalShort Hair 20 40 60 Long Hair 30 10 40 Total 50 50 100 a. Complete a total probability table.b. Complete a row probability tablec. Complete a column probability table.d. The probability that a student does not have long hair. _________e. The probability that a student is male or has short hair. ________f. The probability that a student is a female and has long hair. _________g. The probability that a student is male, given that the student has long hair. _________h. The probability that a student has long hair, given that the student is male. _________i. Of all the female students, the probability that a student has short hair. ________j. Of all students with long hair, the probability that a student is female. _________k. The probability that a student is female or has long hair.…
Non-standard dice can produce interesting distributions of outcomes. Youhave two balanced, six-sided dice. One is a standard die, with faces having 1, 2, 3, 4, 5,and 6 spots. The other die has two faces with 1 spot, two faces with 3 spots, and twofaces with 6 spots. Find the probability distribution for the total number of spots X onthe up-faces when you roll these two dice.

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