Q6 At all times, an urn contains N balls- some white balls and some black balls. At each stage, a coin havingprobability p, 0 0} a Markov Chain? If so, explain why.Q6(ii.) Compute the transition probabilities P;,j: (Hint: At some stage, suppose there are i white balls (and N – iblack balls). Think how you can get i or i – 1 or i +1 white balls in the next stage.)Q6(iii.) Let N = 2. Then the states are 0, 1, 2 and the transition probability matrix is given by(i)2222Find the proportion of the time in each state.

Given that an urn contain N balls, some white balls and some black balls. The probability p of coin…

Answered: Q6 At all times, an urn contains N…

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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Consider an urn with K balls, some of which are white and some are black. At each stage, a fair coin is flipped. If the head appears, then a ball is chosen at random from the urn and is replaced by a white ball. On the other hand, if the tail appears, then a ball is chosen at random from the urn and is replaced by a black ball. Let Xn be the number of white balls in the urn after the n -th stage. Is the process {Xn : n = 0, 1, · · · } a discrete-time Markov chain? If so, specify the state space andtransition probabilities; otherwise explain why it is not a Markov chain.
In an Urn are 5 blue, 3 red and 2 yellow marbles. If you draw 3 marbles, what is the probability that less than 2 will be red if (i). You draw with replacement Soln. (ii). You draw without replacement Soln.
The zebra plays a game in which in every turn she randomly chooses a letter from the set {A,B,C}, independently of other turns, and registers the outcome in a list. 1. Assume that the zebra plays exactly 4 turns, and let X denote the number of distinct outcomes she registers. 2. The first moment of X is 3. The probability that both A and B are registered at some point during the 4 turns she plays is 4. The second moment of X is 2. Now assume that the zebra plays until she registers every possible outcome at least once, that is, once she has registered at least one of each of the outcomes she stops. The expected number of turns she plays is
Q2) 10 cards numbered 1-10 are Shuffled. The top and bottom card are chosen. S: Sum of the two cards. Find the probability distribuhon of S, E(S), E (S²) and Var (x)
A bag contains 3 balls: 1 yellow, 1 red, and 1 green. Suppose I draw 2 balls from the bag with replacement (that is, after drawing the first ball and observing its color, I return it to the bag). Let Y be the event of drawing a yellow ball in a given draw, R be the event of drawing a red ball and G be the event of drawing a green ball.
A box contains 5 white balls and 2 red balls. If three balls are drawn from one box, find the probability that a. One ball is white b. No ball is white c. At least one ball is white d. At most one ball is white
Six digits are chosen randomly from the set {0, 1,2,.....9). a.) What is the probability that all six digits are the same? b.) What is the probability that only 2 digits are the same?
a). A girl is randomly picking flowers in a meadow for a bouquet. She will stop once she has picked 4 dandelions. Suppose that a randomly selected flower is a dandelion with probability 0.70. Find the probability that her bouquet will have exactly 8 flowers in total. b). An entomologist has a collection of 20 insect specimens: 5 are butterflies and 15 are moths. He randomly selects a sample of 6 specimens to study. Find the probability that the sample contains an equal number of butterflies and moths. 2
2. A group of three undergraduate and six graduate students are available to fill certain student government posts. If four students are randomly chosen from this group, find the probability that exactly two undergraduates will be among the four chosen. [Hint: How many ways are there to fill the posts? How many ways satisfy the condition of having exactly TWO undergraduates selected AND hav- ing exactly two graduates selected?]

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