d. Are X and Y independent? You must demonstrate this using the definition.e. What is the correlation between X and Y?f. What is the conditional probability that Person 1 is in seats 1 or 2 given Person 2 is in seat 3? Consider the joint probability mass functionX2Person 1 inPxY(x, y)Person 2 inSeat 1Seat 2Seat 3Seat 4Seat 54. o Seat 10.030.040.060.0821Seat 20.030.080.050.042043Seat 30.040.080.030.07Seat 40.060.050.030.0214Seat 50.080.040.070.022145do

d. Condition for Independence: If P(x,y)=P(x)*P(y), then X and Y are independent. From the joint…

Answered: d. Are X and Y independent? You must…

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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3.12 Mark is deciding which route to take to work. His choices are I = the Interstate and F = Fifth Street.• P(I) = 0.44 and P(F) = 0.55• P(I AND F) = 0 because Mark will take only one route to work.What is the probability of P(I OR F)?
We are interested in analyzing data related to college football. Use S to denote the team is in the SEC and use W to denote a team has a winning season. The probability that a team is in the SEC in the data set is 5.5%. The probability that a team has a winning season is 52.5%. The probability that a team is in the SEC and has a winning season is 3.55%. What percentage of teams are in the SEC or had a winning season? b. What percentage of people teams are in the SEC and did NOT have a winning season? Given a team had a winning season, what is the probability that they are in the SEC? а. с.
The chart below summarizes data related to the number of cars stopped for speeding on Route 195. The chart shows whether the driver being stopped was a teenager or older, and whether the result of the stop was a ticket, written warning, or verbal warning. a) For a randomly selected traffic stop, what is the probability that the result of the stop was a ticket? b) For a randomly selected traffic stop, what is the probability that the driver was a teenager and given a written warning? c) For a randomly selected traffic stop, what is the probability that the car stopped was given a ticket or the driver was 20 or older?
Suppose E= "sum is 5" and F= "exactly one of the dice is even". Are E and F independent? Explain why or why not.
Sub part d and e
Q3/ Explain each of the following branches, then choose the correct answer i. A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and blue balls is: ii. iii. one a. 3 b. 1 28 16 persons shake hands with one another in a party How many shake hands took place? a. 124 b. 120 c. 165 d. 150 - 1/1/12 28 C. 167 168 d. In a college 30% student fail in physics, 25% fail in mathematics and 10% fail in both. One student is chosen at random. The probability that he fails in physics if he has failed in mathematics is
IV. Solve the problem. (don't forget to attached the solution) The Xiaomi brand releases three cellphones that are tested at random. a. Construct the probability distribution of the random variable X (number of defective cellphones). Let G represent non-defective cellphones and, Let F be the defective cellphones. b. Create a histogram representing the distribution
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Consider the joint pmf p(x,y) and marginal pmfs p(x) and p(y) for two discrete random variables X and Y as displayed in the table below. X p(x,y) 1 2 3 p(y) 1 0.125 0.0625 0.1875 0.125 0.5 Y 2 0.0625 0.0625 0.125 0.25 0.5 p(x) 0.1875 0.125 0.3125 0.375 1
Please help to solve this and explain into details please. Thank you.
Q1. Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: What is the probability that at least one girl is born?

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d. Are X and Y independent? You must demonstrate this using the definition. e. What is the correlation between X and Y? f. What is the conditional probability that Person 1 is in seats 1 or 2 given Person 2 is in seat 3?