3.5 Determine the value c so that each of the follow-ing functions can serve as a probability distribution ofthe discrete random variable X:(a) f(x) = c(x² + 4), for x = 0, 1, 2, 3;(b) f(x) = c() (,.), for x = 0, 1, 2.3

We have given that the probability distribution of discrete random variable X. In discrete…

Answered: 3.5 Determine the value c so that each…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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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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The random variables §, 1, $2,... are independent and identically distributed with distribution P(§ = 0) = 1/4 and P(§ = j) = c/j for j = 1,2,3. Let X₁ = 0 and Xn = max(§₁,..., En) for n = 1, 2, .... (a) What value must c take? (b) Explain why {Xn, n = 0, 1, 2,...} is a Markov chain. (c) Write down the transition matrix. (d) Draw the transition diagram and classify the states (aperiodic, transient, re- current, eorgodic, etc). (e) Calculate P(Xn = 0). (f) Calculate P(X4 = 3, X₂ = 1|X₁ = 3).
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3. Determine the value c so that each of the following functions can serve as probability distributions of the discrete random variable X: a. f(x) = c(x² +4) for x = 0,1, 2, 3; 3 b. f(x)%3Dс for x= 0,1, 2 3-x
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3.5 Determine the value c so that each of the follow- ing functions can serve as a probability distribution of the discrete random variable X: (a) f(x) = c(x² + 4), for æ = 0, 1, 2, 3; (b) f(x) = c(;) (,².), for x = 0, 1, 2. 3