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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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).
Solve the below problem. Table 1 contains the probabilities associated with each possible pair of values for Y, and Y, and is known as the joint probability function for Y,and Y2 Table: Probability function for Y, and Y, Yı_ y2 0 1 2 0 1/9 2/9 1/9 2/9 2/9 0 1 | 2 1/9 0 Find F (1, –2) and F(3,3).
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 following table provides the joint probability distribution of of X and Y y3(-1 tion 1 1 3 3 then cov(x,y) none 3. 3. 1130
Q3. Let X and Y be two independent random variables, each representing the number of trials until the first success in a sequence of Bernoulli trials. Evaluate P(X = Y) assuming that the probability of success in a single trial(in case of X and Y both) is 0.4.
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.
The time between busses on Stevens Creek Blvd is 12 minutes. Therefore the wait time of a passenger who arrives randomly at a bus stop is uniformly distributed between 0 and 12 minutes. Find the probability that a person randomly arriving at the bus stop to wait for the bus has a wait time of at most 5 minutes.
10. Two random variables X and Y take on the values i and 2 with probability 1/2' (i = 1,2, ...). Show that the probabilities sum to one. Find the expected value of X and Y.
Suppose that elementary students' ages are uniformly distributed from 5 to 13 years old. The unshaded rectangle below with area 1 depicts this. The shaded rectangle depicts the probability that a randomly selected elementary student will be between ages 10.28 and 11.32 years old. Round all answers to 4 decimal places (if possible).

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