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7. When two dice are tossed, let the random variable X represent the minimum value of the two dice and let the random variable Y represent the absolute value of the difference of the two dice. (a) (b) Find the joint probability function. ]Find the marginal probability density function of X and Y, and determine whether X and Y are independent random variables.

7. When two dice are tossed, let the random variable X represent the minimum value of the two dice and let the random variable Y represent the absolute value of the difference of the two dice. (a) (b) Find the joint probability function. ]Find the marginal probability density function of X and Y, and determine whether X and Y are independent random variables.

A First Course in Probability (10th Edition)
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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Need help with this probability question please Question #7
1. (a) When five dice are rolled, what is the probability that at least 4 "ones" come up? (b) 1 When five dice are rolled, what is the probability of getting a full-house? (ex: aaabb) 2. In a box, there are 3 fair coins, 2 special coins with heads on both sides and 5 special coins with tails on both sides. A coin is randomly selected and flipped. (a) ] If a head comes up, what is the probability that the selected coin is a special coin with heads on both sides? (b) [ 3. Consider a standard deck of 52 cards. Five cards are randomly drawn by each of three players. (a)r (b) When the same coin is flipped again, if a head still comes up, what is the probability that the selected coin is a special coin with heads on both sides? 4. In an office, assume the number of arriving telephone calls has a Poisson distribution with an average rate of 10 calls per hour. (a) [ (b) [ (a) (b) What is the probability that at least one player receives at least one spade? What is the probability that at least one player receives 5 spades? 5. In a country, citizens' annual incomes are normally distributed with a mean of $20,000 and a standard deviation of $4,000. (a) (b) What is the probability that exactly 5 calls arrive in a given 40 minutes? Assume the office opens at 9:00AM. What is the probability that the first call arrives between 9:05AM and 9:15AM? (a) (b) ] When a citizen is randomly surveyed, what is the probability that his annual income is below $17,000? 6. Let X be the continuous random variable with the probability density function f(x) = {(2x+5)/44 if1 ≤x≤5 otherwise ] When 10 citizens are randomly surveyed, what is the probability that their average annual incomes are below $17,000? 7. When two dice are tossed, let the random variable X represent the minimum value of the two dice and let the random variable Y represent the absolute value of the difference of the two dice. Find E(X) and Var (X). ]Find the cumulative distribution function of X. Find the joint probability function. ] Find the marginal probability density function of X and Y, and determine whether X and Y are independent random variables. 15 gram. (a) 8. In a supermarket, the weight of apples has an approximately normal distribution with the mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an approximately normal distribution with the mean of 210 gram and the standard deviation of When an apple and a pear are randomly selected, what is the probability that the apple weights more than the pear? (b) L If Tom randomly buys 30 apples and 20 pears, what is the probability that their total weight exceeds 10kg (10kg = 10, 000g)?
Transcribed Image Text:1. (a) When five dice are rolled, what is the probability that at least 4 "ones" come up? (b) 1 When five dice are rolled, what is the probability of getting a full-house? (ex: aaabb) 2. In a box, there are 3 fair coins, 2 special coins with heads on both sides and 5 special coins with tails on both sides. A coin is randomly selected and flipped. (a) ] If a head comes up, what is the probability that the selected coin is a special coin with heads on both sides? (b) [ 3. Consider a standard deck of 52 cards. Five cards are randomly drawn by each of three players. (a)r (b) When the same coin is flipped again, if a head still comes up, what is the probability that the selected coin is a special coin with heads on both sides? 4. In an office, assume the number of arriving telephone calls has a Poisson distribution with an average rate of 10 calls per hour. (a) [ (b) [ (a) (b) What is the probability that at least one player receives at least one spade? What is the probability that at least one player receives 5 spades? 5. In a country, citizens' annual incomes are normally distributed with a mean of $20,000 and a standard deviation of $4,000. (a) (b) What is the probability that exactly 5 calls arrive in a given 40 minutes? Assume the office opens at 9:00AM. What is the probability that the first call arrives between 9:05AM and 9:15AM? (a) (b) ] When a citizen is randomly surveyed, what is the probability that his annual income is below $17,000? 6. Let X be the continuous random variable with the probability density function f(x) = {(2x+5)/44 if1 ≤x≤5 otherwise ] When 10 citizens are randomly surveyed, what is the probability that their average annual incomes are below $17,000? 7. When two dice are tossed, let the random variable X represent the minimum value of the two dice and let the random variable Y represent the absolute value of the difference of the two dice. Find E(X) and Var (X). ]Find the cumulative distribution function of X. Find the joint probability function. ] Find the marginal probability density function of X and Y, and determine whether X and Y are independent random variables. 15 gram. (a) 8. In a supermarket, the weight of apples has an approximately normal distribution with the mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an approximately normal distribution with the mean of 210 gram and the standard deviation of When an apple and a pear are randomly selected, what is the probability that the apple weights more than the pear? (b) L If Tom randomly buys 30 apples and 20 pears, what is the probability that their total weight exceeds 10kg (10kg = 10, 000g)?
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