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a) A biased coin is tossed, and it is assumed the chance of getting a head, H, is 1/3 (therefore, the chance of getting a tail, T, is 2/3). Consider a random experiment of throwing the coin five times. Let S denote the sample space. describe the elements of S. b) Let X be the random variable that corresponds to the number of the heads coming up in 5 times of tossing. What are the values that the random variable X takes? c) Find the probability that there is 3 tails and 2 heads, that is, P (X=2). d) Find the probability that there are at least 2 heads, that is, P (X> 2).

a) A biased coin is tossed, and it is assumed the chance of getting a head, H, is 1/3 (therefore, the chance of getting a tail, T, is 2/3). Consider a random experiment of throwing the coin five times. Let S denote the sample space. describe the elements of S. b) Let X be the random variable that corresponds to the number of the heads coming up in 5 times of tossing. What are the values that the random variable X takes? c) Find the probability that there is 3 tails and 2 heads, that is, P (X=2). d) Find the probability that there are at least 2 heads, that is, P (X> 2).

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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a) A biased coin is tossed, and it is assumed the chance of getting a head, H, is 1/3 (therefore, the chance of getting a tail, T, is 2/3). Consider a random experiment of throwing the coin five times. Let S denote the sample space. describe the elements of S. b) Let X be the random variable that corresponds to the number of the heads coming up in 5 times of tossing. What are the values that the random variable X takes? c) Find the probability that there is 3 tails and 2 heads, that is, P (X=2). d) Find the probability that there are at least 2 heads, that is, P (X> 2). e) Suppose that for each toss that comes up heads, we win $4, but for each toss that comes up tails, we lose $3. Clearly, the quantity of interest in this situation is our total winning. Let Y denote this quantity. What are the values the random variable Y can take? f) Find P (Y= 6) g) Find P (Y< 0) h) Compute the expectation and the variance of the random variable X. E(X)=? Var(X)=? i) Compute the E(Y) and Var(Y)
Transcribed Image Text:a) A biased coin is tossed, and it is assumed the chance of getting a head, H, is 1/3 (therefore, the chance of getting a tail, T, is 2/3). Consider a random experiment of throwing the coin five times. Let S denote the sample space. describe the elements of S. b) Let X be the random variable that corresponds to the number of the heads coming up in 5 times of tossing. What are the values that the random variable X takes? c) Find the probability that there is 3 tails and 2 heads, that is, P (X=2). d) Find the probability that there are at least 2 heads, that is, P (X> 2). e) Suppose that for each toss that comes up heads, we win $4, but for each toss that comes up tails, we lose $3. Clearly, the quantity of interest in this situation is our total winning. Let Y denote this quantity. What are the values the random variable Y can take? f) Find P (Y= 6) g) Find P (Y< 0) h) Compute the expectation and the variance of the random variable X. E(X)=? Var(X)=? i) Compute the E(Y) and Var(Y)
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