A box contains six cards, labeled 1, 2, 2, 3, 3, and 3. Two cards are chosen at random, with the first cardbeing replaced before the second card is drawn. Let X represent the number on the first card, and let Yrepresent the number on the second card.a. Find the joint probability mass function of X and Y.b. Find the marginal probability mass functions px (x) and py(y).c. Find μχ and μγ·d. Find XY.e. Find Cov(X, Y).

There are six cards in a box - 1,2,2,3,3,3 Two cards are drawn with replacement from the box. X…

Answered: A box contains six cards, labeled 1, 2,…

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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The data for the joint probability mass function of X and Y (two different measurement systems) aregiven in the table below.a) Calculate the marginal distributions of X and Y and plot them.b) Select one of the Y values from the table and find the conditional probability mass function of X for thatY value you have selected and plot it.c) Show whether X and Y are independent or not.d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).
Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows: Find Cov(X, Y). Find ρX,Y .
(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1,2, the waiting time until bus i arrives is denoted by T;, with T independent of T2, and T; has density function fr. (t) = X, exp(-1;t), t>0.
Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. Let Z = X + Y represent the total number of repairs needed. The joint probability mass function of X and Y is as follows: y x 0 1 2 3 0 0.13 0.10 0.07 0.03 1 0.12 0.16 0.08 0.04 2 0.02 0.06 0.08 0.04 3 0.01 0.02 0.02 0.02 Find σZ.. (Round the final answer to three decimal places.)
A salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability 0.3, and his second will lead independently to a sale with probability 0.6. Any sale made is equally likely to be either for the deluxe model, which costs $1000, or the standard model, which costs $500. Determine the probability mass function of X, the total dollar value of all sales.
The probability mass function of a random variable X is given by P(i) = Ck O where i =0,1,2,... where K is some positive value. Find {X=0} A. ec B. ek C. e-e D. e-k A O BO CO
Fourth letter of my surname is "İ".
Suppose that the distribution function of X is given by: (0, b<0 b Osb<1 1 b F(b) =- D=1, Isb<2 2 11 2sb<3 12 b23 1. Determine its corresponding probability mass function. 3 2. Find
a. Verify that f(x) is a valid probability mass function. b. Find the probability that the shuttle will be able to accommodate all ticketed people that show up. c. Say you are the 1st person on the wait list to get on the shuttle (that is to say if less than 4 people with tickets show up, you get a seat). What is the probability that you will be able to board the shuttle?
Let x be the cost ($) of an appetizer and y be the cost of a main course at a certain restaurant for a customer who orders both courses. Suppose that x and y have the following joint distribution: X 5 6 7 Find the probability mass function of x. Find the probability mass function of y. 10 .20 .10 .10 y 15 .15 .15 .10 20 .05 .10 .05
A box contains six cards, labeled 1, 2, 2, 3, 3, and 3. Two cards are chosen at random. Assume the first card is not replaced before the second card is drawn. Let X represent the number on the first card, and let Y represent the number on the second card. Find the joint probability mass function of X and Y and Find the marginal probability mass functions pX(x) and pY (y).
b. The table below shows the joint probability mass function for the discrete random variables X and Y. Y = 1 Y = 2 X = 0 X = 1 X = 2 0.07 0.23 0.18 0.05 0.29 0.18 Calculate and interpret the covariance between variables X and Y i.e. Cov(X,Y).

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