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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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
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.

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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?