Let X Geometric (0.9).(₁Write down the first five values of the probability mass function of X. (This has asimple answer in decimal form.)Px(1) Px(2)Px(3) Px(4)Px (3)Px (5).) Find the conditional probability mass function of X | A, where A is the event "X ≤ 5".(This has a simple answer in fractional form.)Find E[X|X<5).PxA(1) PxA(2) PxA(3) PxA(4) | PX|A(5)1(3).

The probability mass function (PMF) of a geometric distribution with parameter p is given by:…

Answered: Let X~ Geometric (0.9). (₁ Write down…

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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Suppose that you start with an initial fortune of 20 dollars, and you bet one dollar each time. The probability of winning each hand is p. You quit if you reach your goal of L dollars or when you go broke. Let Q(xo) denote that probability that you eventually win. We need to characterize this probability. Next we give a more mathematical description of the problem. Now define your fortune at time n ≥ 1 by - Xn = Xn-1+ I{Y=1} = I{Yn=0} with the initial condition X = x0 ≥0. Let L = N be given, and define T inf{k : Xk = 0 or Xk = L}. Finally, let Q(x0) = P{XT = . L}. Show that X is a Markov chain and obtain its transition probability matrix. Is it irreducible? Use conditional expectations to prove that Q(x)=pQ(x+1) + (1 − p)Q(x − 1), - x = 1, L-1, (1) with Q(0) 0 and Q(L) = 1. = d) Solve the difference equation in (1) analytically. Let P(x0) P{XT = 0}. Determine P(x) directly and show that P(x) + Q(x) = 1. Hint: Use the same form of the difference equation and analytical solution as in…
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