At a particular two-year college, a student has a probability of0.39 of flunking out during a given year, a 0.08 probability ofhaving to repeat the year, and a 0.53 probability of finishing theyear. Use the states shown to the right to complete parts (a)through (c) below.(a) Write a transition matrix. Find F and FR.P=(Type an integer or decimal for each matrix element.)State1234MeaningFreshmanSophomoreHas flunked outHas graduatedF =(Type an integer or decimal for each matrix element. Round to three decimal places as needed.)FR=(Type an integer or decimal for each matrix element. Round to three decimal places as needed.)(b) Find the probability that a freshman will graduate.The probability that a freshman will graduate is(Type an integer or decimal rounded to three decimal places as needed.)(c) Find the expected number of years that a freshman will be in college before graduating or flunking out.The expected number of years is.(Type an integer or decimal rounded to three decimal places as needed.)

Answered: Image /qna-images/answer/21b32e1f-e87f-4c95-b905-7df1e797440c.jpg

Answered: At a particular two-year college, a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A log carrier has a body made from a 4-ft length of reinforced cloth having a patch on each side and a dowel slid through each end to act as handles. The parts-listing matrix for the log carrier is given by the matrix shown below. LC B H C P A = 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 2 0 0 0 Log carrier Body Handles Cloth Patch How many of each primary assembly item are required to fill an order for 500 log carriers and 20 handles?
a. Give the order of the given matrix. b. If A = [a], identify a32 and a23, if possible. 6 -5 - 4 6 Q 3 - 8 1 7 1 5 B 1 9
We want to train a mouse to follow a particular path in the maze (see image 1). To measure the effectiveness of the training, we want to compare the behaviour of the trained mouse to that of a mouse that runs through the maze at random.(a) Construct the matrix T describing the behaviour of the untrained mouse, where tij gives the probability of going to room i when the mouse is in room j. (Note that since the mouse moves randomly if it is in front of two doors, it has a 1/2 probability of going through each of these doors.) (b) Suppose the mouse begins its journey through the maze with a vector of probabilities P(0) = (see image 3) where pi(0) represents the probability of being in room i at the start; so of course we have p1(0)+p2(0)+p3(0)= 1). Show that the probabilities of being in room i after a change of room P(1) are given by P(1)=TP(0). Indications: proceed with a proof on the one hand and on the other hand: start by calculating the probabilities of being in parts 1,2 or 3 after…
Write the payoff matrix for the given game, use Rachel as the row player. Two players, Rachel and Charlie, each have two cards. Rachel has one black card with the number 3 and one red card with the number 5. Charlie has a black card with a 6 written on it and a red card with a 1. They each select one of their cards and simultaneously show the cards. If the cards are the same color, Rachel gets, in dollars, the sum of the two numbers shown. If the cards are different colors, Charlie gets, in dollars, the difference of the two numbers shown.
Find the variables for the matrix.
Find a non-zero, two-by-two matrix such that: 00 A² = 8% 00 A = Hint: There are many different solutions here. Try choosing a random value for one or two of the entries.
Given the Leslie matrix below, what is the population size after 2 timesteps given the starting population size of J= 10, T=10, A=100? Round to nearest whole number. J T A J 0.5 0.5 3.0 T 0.2 0 A O 0.2 0 O a. J=162; T=62; A=1 O b. J=10; T=10; A=100 O c. J=200; T=25; A=5 O d. J=310; T=2; A=3
A car rental service in a certain town has a fleet of about 600 cars, at three locations. A car rented at one location may be returned to any of the three locations. The various fractions of cars returned to the three locations are shown in the matrix to the right. Suppose that on Monday there are 295 cars at the airport (or rented from there), 65 cars at the east side office, and 240 cars at the west side office. What will be the approximate distribution of cars on Wednesday? Cars Rented From: Airport East West 0.95 0.03 0.12 0.00 0.94 0.06 0.05 0.03 0.82 Returned To: Airport East West On Wednesday, 274 cars will be at the airport, 52 cars will be at the East location, and 274 cars will be at the West location. (Round to the nearest integer as needed.)
Class Exercise 1: Players I and II simultaneously call out one of the numbers one or two. Player I's name is Odd; he wins if the sum of the numbers is odd. Player Il's name is Even; she wins if the sum of the numbers is even. The amount paid to the winner by the loser is always the sum of the numbers in rands. Set up the payoff matrix.

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