Q3 Suppose we have two boxes and 2N cards, of which N are blue and N are red. Initially,N of the cards are placed in box 1, and the remainder of the cards are placed in box2. At each trial a card is chosen at random from each of the boxes, and the two cardsare put back in the opposite boxes. Let Xo denote the number of blue cards initiallyin box 1 and, let Xn for n ≥ 1, be the number of blue cards in box 1 after the nthtrial. Find the closed form transition probailities of the Markov chain Xn, n ≥ 0.

Given that we have 2 boxes and 2N cards, of which N are blue and N are red Here we want to…

Answered: Q3 Suppose we have two boxes and 2N…

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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Blood is taken from each of n individuals to be tested for a certain disease. Rather than test each sample separately, a pooled method is used in an attempt to reduce the number of tests needed. Part of each blood sample is taken, and these parts are combined to form a pooled sample. The pooled sample is then tested. If the result is negative, then none of the n individuals has the disease, and no further tests are needed. If the pooled sample tests positive, then each individual is tested to see which of them have the disease. a) Let X represent the number of tests that are carried out. What are the possible values of X? b) Assume that n = 4 individuals are to be tested, and the probability that each has the disease, independent of the others, is p = 0.1. Find µX. c) Repeat part (b) with n = 6and p = 0.2. d) Express µX as a function of n and p. e) The pooled method is more economical than performing individual tests if µX < n. Suppose n = 10. For what values of p is the pooled…
For each of the following find the values of n, x, p and q. DO NOT SOLVE A. When blood donors are randomly selected, 45% of them have blood that is group O. You want to find the probability that when 10 donors are selected, 4 of them are group O. B: random guesses are made for 7 multiple choice questions on a test. Each question has 5 options, 1 of which is correct. You want to find the probability that 3 answers are correct. C: based on a Harris Interactive poll, 20% of adults believe in reincarnation. If 6 adults are randomly selected, find probability that 2 of them do not believe in reincarnation. D: based on American chemical society, there is a 0.9 probability that in tje United States, a randomly selected dollar bill is tainted with traces of cocaine. Assume that 8 dollar bills are randomly selected. Find the probability that at least 5 of them have traces of cocaine.
Buu has 6 different types (named 1 to 6) of chocolates (in large quantity). Now he plays a game to eat those chocolates. He throws a die (of six sides, non-biased, if the die shows 1, he eats chocolate 1. If the die shows 2, he eats chocolate 2 and so on. Now let X be the number of chocolates of type 1 are eaten and Y be the number of chocolates of type 2 are eaten. What is joint PMF of X and Y ?(Total number of times he roll the die is 4.)
Let A and B be the two possible outcomes of an experiment and suppose P(A) = 0.4, P(AUB) = 0.7 And P(B) = P. (i) For what choice of p are A and B mutually exclusive? (ii) For what choice of p are A and B independent?
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Alice has 10 balls (all different). First, she splits them into two piles; then she picks one of the piles with at least two elements,and splits it into two; she repeats this until each pile has only one element.(a) How many steps does this take?(b) Show that the number of different ways in which she can carry out this procedure is[Hint: Imagine the procedure backward.]
A researcher wants to determine whether adolescents spend more time in a day around friends than adults do. He gathers a sample of n =10 adolescents (aged 12-17) and a sample of n =6 adults (aged 25-32). The researcher finds that the average time spent around friends for adolescents is M1= 3 hours with a SS1 of 44. He also finds that the average time spent around friends for adults is M2= 2 hours with a SS2 of 40. a. Do you use a one- or two-tailed test? What is the critical/cut-off t value with an alpha level of α = .01? b. What is the variance? c. What is the estimated standard error? d. What is the value of the t statistic? e. Do we reject or fail to reject the null hypothesis (α = .01)? Why? f. Calculate and report the variance explained ( r2)
A researcher is interested in understanding if there is a difference in the proportion of undergrad and grad students at UCI who prefer online teaching to in person teaching, at the a = 0.05 level. They take 2 samples, first, a sample of 300 undergrad students. The second, is a sample of 172 grad students. Of the undergrads, 186 said they preferred online lectures, and of the graduate students, 104 said that they prefer online lectures. Let p₁ = the proportion of undergrad students who prefer online class and p2 = the proportion of grad students who prefer online lectures. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem). (b) Calculate the test statistic. (c) Calculate the critical value. (d) Draw a picture of the distribution of the test statistic under Ho. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at…
Part 2 Think of four random integers q, r, s, and t selected from 0 through 9. Let a₁ = 0.qrst, where q, r, s, and t are your numbers. Think of four more random integers u, v, w, and x, and add them to the end of a₁ to create a2 = 0.qrstuvwx. Repeat this process to generate a3, 94, and a5. If this process is continued infinitely many times, then explain whether or not the sequence {an} converges, diverges, or it is impossible to determine.
Buu has 6 different types (named 1 to 6) of chocolates (in large quantity). Now he plays a game to eat those chocolates. He throws a die (of six sides, non-biased, if the die shows 1, he eats chocolate 1. If the die shows 2, he eats chocolate 2 and so on. Now let X be the number of chocolates of type 1 are eaten and Y be the number of chocolates of type 2 are eaten. What is joint PMF of X and Y?

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