Give an example of a discrete random variable X such that Sx contains exactly two points, and a number c > 0 such that the Markov's inequality is tight, i.e. E(X) P(X > c) =

Q: The number of items produced in a factory during a week is known to be a random variable with mean…

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Q: ou have a markov chain and you can assume that P(X0 = 1) = P(X0 = 2) = 1/2 and that the matrix looks…

A: P(X0 = 1) = P(X0 = 2) = 12 P=12121323

Q: Let X1, ..., X20 be independent Poisson random variables with mean one. 1 2 (a) Use the Markov…

A: X~Pois(Mean = 1)

Q: Q1: Prove (a) Markov's Inequality for non-negative continuous random variables U. (b) Chebeshey's…

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Q: A Markov chain has the transition probability matrix [0.3 0.2 0.5 0.5 0.1 0.4 0.5 0.2 0.3 What is Pr…

A: For the given , transition probability matrix. We need to find the probability:  Pr(X2 = 1, X3 = 2 |…

Q: where c is a constant that makes this a valid p.d.f.. Let Y = EX?. Use Markov's inequality to find…

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Q: Specify the classes of the Markov Chain, and determine whether they are transient or recurrent.…

A: Given the Markov Chain,  P2=000100011212000010

Q: Prove that the square of a Markov matrix is also a Markov matrix.

A: An n×n matrix is called Markov matrix if all entries are non negative and the sum of each column…

Q: A Doubly stochastic matrix is a stochastic matrix M of which the columns also sum to 1, i.e., Mij…

A: a) To show that the row vector  with entries for all is a stationary distribution for the Markov…

Q: Let X be a Poisson random variable with mean λ = 20. Estimate the probability P(X ≥25) based on: (a)…

A: To estimate the probability P(X≥25) for a Poisson random variable X with mean λ=20, we will use four…

Q: Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with -ix (1/2 1/2 0 0 1/7 0 3/7 3/7 0…

A: Given that  be the Markov chain on state space  with transition matrix:

Q: is Find the vector of stable probabilities for the Markov chain whose transition matrix 0.1 0.6 0.3…

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Q: Suppose that X1, X2, X3 are independent and identically distributed random variables with…

A: # Given CDF of random variable x  F(x)=1-2^-x     : x>0  let y=max(x1,X2,x3)   To find…

Q: Find the vector of stable probabilities for the Markov chain whose transition matrix is

A: Let the stable vector of probabilities be; W=xyzwhere;x+y+z=1 Let; P=01000.60.4100

Q: Show that if X is not a deterministic random variable, then H(X) is strictly positive. What happens…

A: Suppose a random variable takes values on k numbers {a1 , a2,...., ak} with corresponding…

Q: This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese…

A: Given Information: Consider that state 1 is Chinese (C), state 2 is Greek (G) and state 3 is Italian…

Q: Which statements are true? Select one or more: a. Markov’s inequality is only useful if I am…

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Q: C)

A: a) If you find the solution doubtful or doesn't match with your answer provided, or you feel that I…

Q: For the following Markov models: ; b) find the stationary probability distribution on paper 5A An…

A: Note : We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: A Markov chain model for a species has four states: State 0 (Lower Risk), State 1 (Vulnerable),…

A: Given a Markov chain model for a species has four states : State 0 (Lower Risk), State 1…