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a. Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. Wht type of random variable is Y? What is $P(Y=3)? What is the expected number of sixes?

a. Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. Wht type of random variable is Y? What is $P(Y=3)? What is the expected number of sixes?

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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Chapters: Normal and Exponential random variables. Q: For each of the following descriptions of a random variable, indicate whether it can best be modeled by binomial, geometric, uniform, exponential or normal. Also, answer the associated question. a. Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. Wht type of random variable is Y? What is $P(Y=3)? What is the expected number of sixes? b. Suppose a stop light has a red light that lasts for 60 seconds a green light that lasts for 30 seconds and a yellow light that lasts for 5 seconds. When you first observe the stop light, it is red. Let X denote the time until the light turns green. What type of rv would be used to model X? What is the mean? c. Customers arrive at a teller's window at a uniform rate 5 per hour. Let X be the length in minutes of time that the teller has to wait until they see their first customer after starting their shift. What type of rv is X? What is its mean? Find the probability that the teller waits less than 10 minutes for their first customer.
Transcribed Image Text:Chapters: Normal and Exponential random variables. Q: For each of the following descriptions of a random variable, indicate whether it can best be modeled by binomial, geometric, uniform, exponential or normal. Also, answer the associated question. a. Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. Wht type of random variable is Y? What is $P(Y=3)? What is the expected number of sixes? b. Suppose a stop light has a red light that lasts for 60 seconds a green light that lasts for 30 seconds and a yellow light that lasts for 5 seconds. When you first observe the stop light, it is red. Let X denote the time until the light turns green. What type of rv would be used to model X? What is the mean? c. Customers arrive at a teller's window at a uniform rate 5 per hour. Let X be the length in minutes of time that the teller has to wait until they see their first customer after starting their shift. What type of rv is X? What is its mean? Find the probability that the teller waits less than 10 minutes for their first customer.
d. A coin is tossed until a head is observed. Let X denote the total number of tails observed during the experiment. What type of rv is X? What is its mean? Find P(X < 3). f. Let X be the recorded body temperature of a healthy adult in degrees Fahrenheit. What type of rv is X? Estimate its mean and standard deviation, based on your knowledge of body temperatures.
Transcribed Image Text:d. A coin is tossed until a head is observed. Let X denote the total number of tails observed during the experiment. What type of rv is X? What is its mean? Find P(X < 3). f. Let X be the recorded body temperature of a healthy adult in degrees Fahrenheit. What type of rv is X? Estimate its mean and standard deviation, based on your knowledge of body temperatures.
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