Problem 1 Suppose a population has N people. Among them, N1 are males, and No are females. Among the males, T¡ are taller than 6 feet. Among the females, To are taller than 6 feet. Suppose we randomly sample a person from the population. Let A be the event that the person is male. Let B be the event that the person is taller than 6 feet. Using the numbers N, N1, No, T1, To, calculate or prove the following: (1) Calculate P(A), P(B), P(A|B), P(B|A), P(AN B). (2) Show that P(An B) = P(A)P(B|A) = P(B)P(A|B). This is called chain rule. (3) Show that P(B) = P(A)P(B|A) + P(A^)P(B|A°). This is called rule of total probability. (4) Show that %3D P(AN B) P(B) P(A)P(B|A) P(A)P(B|A)+ P(A©)P(B|A®)' P(A|B)

Problem 1 Suppose a population has N people. Among them, N1 are males, and No are females. Among the males, T¡ are taller than 6 feet. Among the females, To are taller than 6 feet. Suppose we randomly sample a person from the population. Let A be the event that the person is male. Let B be the event that the person is taller than 6 feet. Using the numbers N, N1, No, T1, To, calculate or prove the following: (1) Calculate P(A), P(B), P(A|B), P(B|A), P(AN B). (2) Show that P(An B) = P(A)P(B|A) = P(B)P(A|B). This is called chain rule. (3) Show that P(B) = P(A)P(B|A) + P(A^)P(B|A°). This is called rule of total probability. (4) Show that %3D P(AN B) P(B) P(A)P(B|A) P(A)P(B|A)+ P(A©)P(B|A®)' P(A|B)

Name: Problem 1 Suppose a population has N people. Among them, N1 are males
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Description: Problem 1 Suppose a population has N people. Among them, N1 are males, and No are females.Among the males, Tị are taller than 6 feet. Among the females, To are taller than 6 feet. Supposewe randomly sample a person from the population. Let A be the

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

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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Question

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Problem 1 Suppose a population has N people. Among them, N1 are males, and No are females.
Among the males, Tị are taller than 6 feet. Among the females, To are taller than 6 feet. Suppose
we randomly sample a person from the population. Let A be the event that the person is male.
Let B be the event that the person is taller than 6 feet.
Using the numbers N, N1, No, T1, To, calculate or prove the following:
(1) Caleulate P(A), P(B), P(A| B), P(Β | Α), P(A ) .
(2) Show that P(An B) = P(A)P(B|A) = P(B)P(A|B). This is called chain rule.
(3) Show that P(B) = P(A)P(B|A) + P(A°)P(B|A°). This is called rule of total probability.
(4) Show that
P(AN B)
P(B)
P(A)P(B|A)
P(A)P(B|A)+ P(A^)P(B|A°)°
P(A|B)

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