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).

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).

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...

See similar textbooks

Similar questions

Let X be the number of tails in three flips of a fair coin. Let Y be the outcome of a roll of a fair six-sided die. Assume X and Y are independent. Give the joint probability mass function of X,Y. Be precise about the values for which the joint probability mass function is defined.
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 .
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 $500. Determine the probability mass function of X, the total dollar value of all sales.
Let Y1 and Y2 be independent Poisson random variable with means , and 22, respectively. Using a moment generating function technique, find the probability density function of U=Y1+Y2. Hence, find the conditional probability function of Y1 given Y1+ Y2 = m. 4.
The joint probability mass function of X and Y is given by p(1, 1) = 0.05 p(2, 1) = 0.1 p(1,2) = 0.05 p(1, 3) = 0.05 p(2,2) = 0 p(2, 3) = 0.05 p(3, 1) = 0.05 p(3,2) = 0.1 p(3, 3) = 0.55 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = ☐ P(Y = 2X = 2) = P(Y = 3|X = 2) (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X + Y > 2) = P(XY = 2) = P(¥ > 1) = |
Let x be the cost ($) 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 6 balls, 4 of which are red. I randomly select 3 balls from the box. Find the probability mass function of getting 2 red balls?