In a strange game, a turn can end with the player earning either 0, 3, or 7 points. Each turn is either "easy" or "hard", based on the flip of a weighted coin. If a turn is "easy", the point likelihoods are as follows: the player earns 0 points 20% of the time the player earns 3 points 30% of the time the player earns 7 points 50% of the time If a turn is "hard", the point likelihoods are as follows: the player earns 0 points 70% of the time the player earns 3 points 20% of the time the player earns 7 points 10% of the time Suppose that the likelihood a turn is "easy" is 35%. In the following problems we ask you to give an expression. This expression should contain numeric values. For example, the expression that captures the probability that two consecutive turns are easy is (0.35*0.35). 1. Let I be a random variable which represents the points earned in a given turn. Give an expression for the expected value of T. You do not need to evaluate this expression. Show how you derived this expression. 2. Let I be a random variable which represents the points earned in a given turn. Give an expression for the probability that T=0. You do not need to evaluate this expression. Show how you derived this expression.
In a strange game, a turn can end with the player earning either 0, 3, or 7 points. Each turn is either "easy" or "hard", based on the flip of a weighted coin. If a turn is "easy", the point likelihoods are as follows: the player earns 0 points 20% of the time the player earns 3 points 30% of the time the player earns 7 points 50% of the time If a turn is "hard", the point likelihoods are as follows: the player earns 0 points 70% of the time the player earns 3 points 20% of the time the player earns 7 points 10% of the time Suppose that the likelihood a turn is "easy" is 35%. In the following problems we ask you to give an expression. This expression should contain numeric values. For example, the expression that captures the probability that two consecutive turns are easy is (0.35*0.35). 1. Let I be a random variable which represents the points earned in a given turn. Give an expression for the expected value of T. You do not need to evaluate this expression. Show how you derived this expression. 2. Let I be a random variable which represents the points earned in a given turn. Give an expression for the probability that T=0. You do not need to evaluate this expression. Show how you derived this expression.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text:Q#11:
In a strange game, a turn can end with the player earning either 0, 3, or 7 points. Each
turn is either "easy" or "hard", based on the flip of a weighted coin.
If a turn is "easy", the point likelihoods are as follows:
the player earns 0 points 20% of the time
the player earns 3 points 30% of the time
the player earns 7 points 50% of the time
If a turn is "hard", the point likelihoods are as follows:
the player earns 0 points 70% of the time
the player earns 3 points 20% of the time
the player earns 7 points 10% of the time
Suppose that the likelihood a turn is "easy" is 35%.
In the following problems we ask you to give an expression. This expression should
contain numeric values. For example, the expression that captures the probability that
two consecutive turns are easy is (0.35*0.35).
1. Let I be a random variable which represents the points earned in a given turn. Give
an expression for the expected value of T. You do not need to evaluate this expression.
Show how you derived this expression.
2. Let I be a random variable which represents the points earned in a given turn. Give
an expression for the probability that T=0. You do not need to evaluate this expression.
Show how you derived this expression.
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