Problem 2. Suppose I have 10 cards, labeled 1 through 10. They're completely shuffled so every permu-tation is equally likely. You draw 2 cards and give me the smaller card. Let X be the random variablethat is my card's value.(a) What is the probability mass function (pmf) and cumulative distribution function (cdf) of my card'sface value, X? We'll denote these p(x) and F(x) respectively. Plot the cdf.(b) What is the expected value of X? We'll denote this E[X].

Suppose I have 10 cards, labeled 1 through 10. They're completely shuffled so every permutation is…

Answered: Problem 2. Suppose I have 10 cards,…

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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Given the following probability distribution for the number of semesters of Math a (non-Math major) college student will take as they earn their degree: x:number of semesters of Math 1 2 3 4 P(x) 0.25 0.45 0.20 0.10 What is the probability that a randomly selected (non-Math major) college student will have taken exactly 3 semesters of Math? Show how you calculated your result here (type in what you typed on your calculator or computer, etc) Calculation: __________ Now type in your final simplified or rounded answer, if necessary round your answer to four decimal places. P(exactly 3 semesters of Math) = _____________
1. Toss a coin twice .Write the probability distribution of the random variable (a)X = 3( Number of Heads - Number of Tails). Then find (1) P( X >0) ; (ii) E(X), Var(X) and S.D (X).
Suppose a coin with Pr[H]=4/5Pr[H]=4/5 is flipped 4 times. Answer the following questions: 1. What is the probability exactly 2 heads were flipped? 2. What is the probability that heads then tails then heads then tails was flipped?
Question 4 a) A bowl contains six white chips, three red chips and one blue chip. A chip is taken at random from the bowl. Let the random variable X = 1 if a white chip is chosen, let X = 5 if a red chip is chosen and let X = 10 if a blue chip is chosen. Find: i) The probability function f (x) of X. ii) The distribution function F(x) of X. iii) E(X). iv) E(3X² + 5). v) Var(X) b) A discrete random variable X has probability function f (x) = k(x + 1)²,x = 0,1,2. i) Find the value of k. ii) Find E (5X + 3), E (X²) and Var(3X – 2). c) The discrete random variable X represents the number of days spent by a certain 5-х patient in a hospital. The probability function of X is f(x) : -,x = 1,2,3,4. The 10 patient receives $200 from an insurance company for each of the first two days in hospital, and $100 for each day after the first two days. What is the expected amount received?
1. The random variables X and Y describe the outcome of two independent tosses with a dice. Let Z = X+Y be the sum of the results. Determine (a) The probability distributions for X, Y and Z. (b) H(X), H(Y) and H(Z). (c) H(YX), H(Z|X) and H(X|Z). (d) I(X;Y) and I(X; Z).
If X and Y have the joint probability distributionf(x, y) = 14 for x = −3 and y = −5, x = −1 andy = −1, x = 1 and y = 1, and x = 3 and y = 5, findcov(X, Y).
The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.
Solve the following 1. If the joint probability distribution of X and Yis given by x+y f(x, y) for x = 0,2,3; y = 0,1,2 30 Find
2. We have two fair dice, one red and one blue. When we roll them together, the outcome can be shown as an order pair, (R, B) where R and B are numbers from the red and the blue die, respectively. Let X be a random variable defined by X(R, B) = R - B where R and B are numbers from red and blue dice, respectively. (a) What is the probability mass function for the random variable? Show that as a table.
Is P(S = s) = fs(s) = 1+11+1 ; s = 0,1,2,... 0; е. w. a discrete probability function? Why or why not?
You're a production engineer for a small manufacturing facility that contains three machines (M1, M2, M3) that are arranged in series. That is, raw material enters M, and leaves M3 as a finished part. Time between failures (in days) for machine M; is described with random variables T;, which are assumed to follow exponential distributions with the parameters found in the table below. The reliability, R;(t), or the probability that failure occurs after time t, of Mi is calculated as 1 - F;(t). And recall that F;(t) is the cumulative probability distribution for Mi evaluated at time t. a. Calculate the average failure time for the three machines. b. Calculate R;(14), or reliability at 14 days of operation, for each machine. Calculate the system reliability, Rs(14), for this series system (that is, the probability that raw material can enter M, and leave M3, at 14 days of operation). с. M1 М M3 M1 M2 M3 0.026 0.012 0.019
A committe of size 3 to be selected at random from 4 chemists and 5 physicists , Find the probability that : E (x)=? а- 16/9 b- 15/9 с-3/4 d- 8/7 e- 4/3

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