A survey investigates the relation between the economic activity and gender. Let the random variable the economic activity of a (randomly selected) person in termns of dollars spent per year (in thousands) G be the gender of this (randomly selected) person taking a value of 0 for women and 1 for men. The s finds that the cumulative distribution function of the economic activity of women is given by FXIG(z | 0) r/100 for 0srs 10, %3!
A survey investigates the relation between the economic activity and gender. Let the random variable the economic activity of a (randomly selected) person in termns of dollars spent per year (in thousands) G be the gender of this (randomly selected) person taking a value of 0 for women and 1 for men. The s finds that the cumulative distribution function of the economic activity of women is given by FXIG(z | 0) r/100 for 0srs 10, %3!
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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![Problem 5 (.
A survey investigates the relation between the economic activity and gender. Let the random variable X be
the economic activity of a (randomly selected) person in terms of dollars spent per year (in thousands). Let
G be the gender of this (randomly selected) person taking a value of 0 for women and 1 for men. The study
finds that the cumulative distribution function of the economic activity of women is given by'
FxiG(z | 0) = r/100 for 0srs 10,
and the cumulative distribution of the economic activity of men is given by
FxG(r | 1) = 1/10 for 0srs 10.
Additionally, 60% of the population is women i.e. P(G = 0) 0.6. Based on this information, answer the
following questions.
1. What is the probability density function of the economic activity i.e. what is fx(x)? 2
2. Given that a person's economic activity is more than 5,000 dollars, what is the probability that this
person is a man? In other words, find P(G 1|X 2 5).
3. What is the expected economic activity of a person i.e. what is E[X]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75f6df43-99e5-49ed-a68c-ec07e10ce1e5%2F12477767-2f38-4c7c-9dfc-06138c173295%2Fjzk2gnf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 5 (.
A survey investigates the relation between the economic activity and gender. Let the random variable X be
the economic activity of a (randomly selected) person in terms of dollars spent per year (in thousands). Let
G be the gender of this (randomly selected) person taking a value of 0 for women and 1 for men. The study
finds that the cumulative distribution function of the economic activity of women is given by'
FxiG(z | 0) = r/100 for 0srs 10,
and the cumulative distribution of the economic activity of men is given by
FxG(r | 1) = 1/10 for 0srs 10.
Additionally, 60% of the population is women i.e. P(G = 0) 0.6. Based on this information, answer the
following questions.
1. What is the probability density function of the economic activity i.e. what is fx(x)? 2
2. Given that a person's economic activity is more than 5,000 dollars, what is the probability that this
person is a man? In other words, find P(G 1|X 2 5).
3. What is the expected economic activity of a person i.e. what is E[X]?
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