There are two different point of view of probability: a frequentist and a Bayesian point of view. Select all statement(s) that is(are) true.

Group of answer choices

In public health problem, we only use Frequentist point of view of probability.

In public health problem, we only use Bayesian point of view of probability.

Frequentist point of viewof probability is based ondegrees of belief whereas Bayesian point of view of probability is based on number of trials.

In public health problem, we both use Frequentist and Bayesian point of views of probability and most of the mathematical rules are the same in the two point of views.

After reading a review article written by an expert in the field about a promising new treatment never been administered, you think the probability of the new treatment being effective is high, i.e., > 0.7.

In this example, you are using Frequentist point of view of probability.

A physician met with a patient with a very rare disease. After consulting with other experts and searching through published literature, the physician finds a similar case reported in 1790 in France. The physician thinks the probability that her patient has this rare syndrome is high, i.e., > 0.8.

In this example, the physician is using Bayesian point of view of probability.

In a population of a hospital patients, the probability that a randomly selected patient will have a heart disease is 15%. Moreover, the probability that a patient is a heavy smoker given that he or she has a heart disease is 70%. What is the probability that a patient randomly selected from the population will be a heavy smoker and have a heart disease?

Group of answer choices

8.5%

10.5%

50%

85%

Two events A and B are mutually exclusive if:

Group of answer choices

A = {a subject has a flu} and B = {a subject is male}

They are independent.

A = {a subject has a body mass index over 25} and B = {a subject has a body mass index below 15}

A = {a subject weight is over 100} and B = {a subject weight is below 120}

The following table presents table of five hundred employees of plant manufacturing a product suspected to cause respiratory diseases. The employees are interviewed relative to their levels of exposure to the product and the presence/absence of respiratory problems. What is Pr(No ExposureorNo Respiratory Problems)?

Which of the following represents a continuous variable?

Group of answer choices

The blood type of students enrolled in this class.

The number of males in a randomly selected family.

The diastolic blood pressure of students enrolled in FIU

The number of correct answers on a quiz.

This table will be used for Questions 7 and 8. Suppose the probability that a person will develop hypertension over a life time is 0.2. Let random variable X represent number of hypertensives over a lifetime among 3 students graduating from the same high school class. A student calculates the following as the probability mass function for X. We figured out that the above probability mass function is incorrect. What is the correct reason why the above probability mass function is incorrect?

Group of answer choices

Pr(X=0) + Pr(X=1) should equal to 0.95

Pr(X=2) + Pr(X=3) should equal to 0.05

Pr(X=0) + Pr(X=1) + Pr(X=2) + Pr(X=3) should equal to 1.0

Pr(X=1) should equal to 2.0 - ( Pr(X=0) + Pr(X=2) + Pr(X=3) )

None of the above statements are true.

From the Question 7 distribution table, we further figured out Pr(X=0) and Pr(X=1) are incorrectly calculated. What is the correct calculation for Pr(X=1)?

Group of answer choices

0.512

0.384

0.096

0.008

This information will be used for Questions 9, 10, and 11. Suppose that for boys, mean Systolic Blood Pressure (SBP) is 95 mm Hg at 3 years of age and increases 1.5 mm Hg per year up to the age of 13. Also assume that blood pressure is normally distributed and that the standard deviation is 12 mm Hg for all age-sex group. Let random variable Y represent SBP for an 11-year old boy. Note that Y ~ N(107, 144) and Z ~ N(0, 1). Select a correct statement:

Group of answer choices

Pr(Y = 107) = Pr(Z = 0) = 0.5

Pr(Y ? 107) = Pr(Z ? 0) = 0.5

Pr(Y ? 0) = Pr(Z ? 107) = 0.5

Pr(Y = 0) = Pr(Z = 107) = 0.5

Using information from Question 9, what is the probability that an 11-year old boy will have SBP higher than 131 mm Hg?

Group of answer choices

0.97725

0.76324

0.21353

0.02275

Question 5 10 pts The following table presents table of five hundred employees of plant manufacturing a product suspected to cause respiratory diseases. The employees are interviewed relative to their levels of exposure to the product and the presence/absence of respiratory problems. Exposure Respiratory problems Yes No Total High 185 120 305 Limited 33 73 106 None 17 72 89 Total 235 265 500 What is Pr(No Exposure or No Respiratory Problems)? 0.152 0 0.37 0.564 0 0.71Question 7 7 pts This table will be used for Questions 7 and 8. Suppose the probability that a person will develop hypertension over a life time is 0.2. Let random variable X represent number of hypertensives over a lifetime among 3 students graduating from the same high school class. A student calculates the following as the probability mass function for X. 0.3 0.2 0.096 0.008 We figured out that the above probability mass function is incorrect. What is the correct reason why the above probability mass function is incorrect? O Pr(X=0) + Pr(X=1) should equal to 0.95 Pr(X=2) + Pr(X=3) should equal to 0.05 ( Pr(X=0) + Pr(X=1) + Pr(X=2) + Pr(X=3) should equal to 1.0 O Pr(X=1) should equal to 2.0 - ( Pr(X=0) + Pr(X=2) + Pr(X=3) ) O None of the above statements are true. Question 8 10 ptsQuestion 2 5 pts There are two different point of view of probability: a frequentist and a Bayesian point of view. Select all statement(s) that is(are) true. In public health problem, we only use Frequentist point of view of probability. In public health problem, we only use Bayesian point of view of probability. Frequentist point of view of probability is based on degrees of belief whereas Bayesian point of view of probability is based on number of trials. In public health problem, we both use Frequentist and Bayesian point of views of probability and most of the mathematical rules are the same in the two point of views. After reading a review article written by an expert in the field about a promising new treatment never been administered, you think the probability of the new treatment being effective is high, i.e., > 0.7 In this example, you are using Frequentist point of view of probability. A physician met with a patient with a very rare disease. After consulting with other experts and searching through published literature, the physician finds a similar case reported in 1790 in France. The physician thinks the probability that her patient has this rare syndrome is high, i.e., > 0.8. "In this example, the physician is using Bayesian point of view of probability. Question 3 10 ptsQuestion 3 10 pts In a population of a hospital patients, the probability that a randomly selected patient will have a heart disease is 15%. Moreover, the probability that a patient is a heavy smoker given that he or she has a heart disease is 70%. What is the probability that a patient randomly selected from the population will be a heavy smoker and have a heart disease? 0 8.5% 0 10 5% @ 50% 85%Question 4 Two events A and B are mutually exclusive if: A = [a subject has a flu] and B = [a subject is male] They are independent. P(An B) = 1.0 A = [a subject has a body mass index over 25] and B - [a subject has a body mass index below 15] A = [a subject weight is over 100] and B - [a subject weight is below 120]Question 6 Which of the following represents a continuous variable? The blood type of students enrolled in this class. The number of males in a randomly selected family. The diastolic blood pressure of students enrolled in FIU The number of correct answers on a quiz.10 pts From the Question 7 distribution table, we further figured out Pr(X-0) and Pr(X-1) are incorrectly calculated. What is the correct calculation for Pr(X=1)? 0.512 0 0.384 1 0.096 0 0.008Question 9 7 pts This information will be used for Questions 9, 10, and 11. Suppose that for boys, mean Systolic Blood Pressure (SBP) is 95 mm Hg at 3 years of age and increases 1.5 mm Hg per year up to the age of 13. Also assume that blood pressure is normally distributed and that the standard deviation is 12 mm Hg for all age-sex group. Let random variable Y represent SBP for an 11-year old boy. Note that Y ~ N(107, 144) and Z - N(0, 1). Select a correct statement: Pr(Y = 107) = Pr(Z = 0) = 0.5 Pr(Y = 107) = Pr(Z s 0) = 0.5 Pr(Y = 0) = Pr(Z = 107) = 0.5 Pr(Y = 0) = Pr(Z = 107) = 0.5Question 10 10 pts Using the information from Question 9, how do we calculate the probability that an 11-year old boy will have SBP less or equal to 131 mm Hg using Y and Z? Pr(Y s 13 1) = Pr(Z s 131) O Pr(Y s 131) = Pr(Z