Below is a joint probability distribution for the members of a state congress bylegislative group and political party. The "other" category includes Independents andvacancies.DemocraticP₁RepublicanP₂OtherP3P (C₁)RepC₁0.3860.4270.0050.818GroupSenatorC₂0.0990.0810.0020.182P (P₁)0.4850.5080.0071.000a. Determine P (P₁), P (C₁), and P (P₁ &C₁).P(P₁)=[P(C₁)=[(Type an integer or a decimal.)

Given the joint probability distribution for the members of the state congress by legislative group…

Answered: Below is a joint probability…

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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The following contingency table shows statistics marks (columns) and three sections (rows) for 480 students. Develop a joint probability table and use it to answer the following questions. Section Marks Low Average High Section A 82 40 55 Section B 37 64 63 Section C 48 40 51 For a randomly chosen student, find the probability that: The student is a high scorer. The student is from section C. The student scored high marks given that student is from section B. The student is from section A given that student scored average marks. Solve each of the above?
Every business day, Michael's alarm goes off at 06:30. The probability he hits the snooze button is 20%. a. Give the discrete probability distribution for the event that Michael's alarm does or does not go off on a business day. What type of random variable is this? Explain. b. In 8 business days, what is the probability Michael hits the snooze button at least one time? c. In 80 business days, how many times would we expect Michael to hit the snooze button? What is the associated variance?
The following table provides the joint probability distribution for the 98th Congress by political party. Reps C1 Senators C2 TOTAL __________________ Democrats P1 0.500 0.084 Republicans P2 0.313 0.103 TOTAL Determine P(P1) ___________ P(C2) _____________ P( P1 & C2) ___________
Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren't present in legitimate records. Some patterns, like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford's law. Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit cannot be 0). First digit x; Probability Pi 1 0.301 2 0.176 3 4 0.125 0.097 What is the expected value of X? Interpret this value. 5 0.079 6 0.067 7 0.058 8 0.051 9 0.046 ○ μx = 5. In many, many randomly chosen legitimate records, the average of the first digit would be about 5. ○ μx = 3.441. In many, many randomly chosen legitimate records, the average of the first digit would be about 3.441. μx 5. In a randomly chosen legitimate record, the average of the first digit would…
The table below shows the soft drinks preferences of people in three age groups. If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and drinks cola. Cola Root beer Lemon-lime Under 21 yrs of age 40 25 20 Between 21 and 40 35 20 30 Over 40 yrs of age 20 30 35
The national soccer team headed by Daniel plays soccer 3 times a week. The team plays soccer, 0 days is 0.2 probability, they play 1 day is 0.25 probability, they play 2 days is 0.5, and they play 3 days otherwise. a. Construct a probability distribution table. b. Find the long-term average, or expected value of the days per week the national soccer team plays soccer.
The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group-blood group combinations. Blood Group A B АВ 1 0.082 0.114 0.011 0.004 Ethnic Group 2 0.127 0.141 0.018 0.003 3 0.215 0.202 0.063 0.020 Suppose that an individual is randomly selected from the population, and define events by A = {type A selected}, B = {type B selected}, and C = {ethnic group 3 selected}. (a) Calculate P(A), P(C), and P(A n C). (Enter your answers to three decimal places.) P(A) = Р(С) P(A n C) = = (b) Calculate both P(A|C) and P(C|A). (Round your answers to three decimal places.) P(A|C) %3D P(C|A) %3D Explain in context what each of these probabilities represents. (Select all that apply.) If a person has type A blood, the probability that he is from ethnic group 3 is given by P(C|A). If we know that the individual came from ethnic…
The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group-blood group combinations. O 0.082 0.141 Blood Group A B 0.100 0.009 AB 0.004 0.141 0.018 0.005 0.215 0.204 0.061 0.020 Ethnic Group 1 2 3 Suppose that an individual is randomly selected from the population, and define events by A = {type A selected}, B = {type B selected}, and C = {ethnic group 3 selected}. (a) Calculate P(A), P(C), and P(An C). (Enter your answers to three decimal places.) P(A) = P(C) = P(ANC) = (b) Calculate both P(AIC) and P(CIA). (Round your answers to three decimal places.) P(AIC) = P(CIA) = Explain in context what each of these probabilities represents. (Select all that apply.) If a person has type B blood, the probability that he is from ethnic group 3 is given by P(AIC). If we know that the individual came from ethnic group…
The population of a particular country consists of three eth- nic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group-blood group combinations. Blood Group 0 A B AB 1 .082 .106 .008 .004 Ethnic Group 2 .135 .141 .018 .006 3 215 200 .065 .020 Suppose that an individual is randomly selected from the population, and define events by A = {type A selected}, B = {type B selected}, and C = {ethnic group 3 selected}. a. Calculate P(A), P(C), and P(AC). b. Calculate both P(A|C) and P(C|A), and explain in con- text what each of these probabilities represents. c. If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1?
An urn contains 2 red and 2 green marbles. We pick a marble, record its color, and replace it. We repeat this procedure a second and a third time. The probability distribution for the number of red marbles is given below. Number of red marbles 0 1 2 3 Probability 1/8 3/8 3/8 1/8 For this distribution, the probability of 2 or more red marbles is given by: a. 1/4. b. 3/8. c. 6/8. d. 1/2.
The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group-blood group combinations. Blood Group O A B AB 1 0.082 0.110 0.013 0.004 Ethnic Group 2 3 0.131 0.215 0.141 0.190 0.018 0.001 0.075 0.020 Suppose that an individual is randomly selected from the population, and define events by A = {type A selected}, B = {type B selected}, and C = {ethnic group 3 selected}. (a) Calculate P(A), P(C), and P(A n C). (Enter your answers to three decimal places.) P(A) P(C) = = P(An C) = (b) Calculate both P(A|C) and P(CIA). (Round your answers to three decimal places.) = P(A|C) P(C|A) = Explain in context what each of these probabilities represents. (Select all that apply.) If we know that the individual came from ethnic group 3, the probability that he has type A blood is given by P(CIA). If a person has type A blood,…
The numbers of domestic and international flights for three airlines for the year 2012 are given in the table. Find the probability that a domestic flight is operated by Airline B. Airline A B C Total Domestic International Total 517,971 120,976 638,947 729,981 96,611 826,592 527,769 135,211 662,980 1,775,721 352,798 2,128,519 The probability that a domestic flight is operated by Airline B is (Round to four decimal places as needed.)

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