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Quiz 7: Discrete Random Variables

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Quiz

This quiz tests materials in the section called “Discrete random variables”. If you are struggling with the questions go back and re-read the relevant material.

A variable \(Z\) has the following distribution:

\(z\)

P(Z=\(z\))

1

0.3

2

0.2

3

0.4

4

0.1

Question 1: Calculate \(E(Z)\)

Choose the correct answer:

  1. \(6.3\)

  2. \(1.01\)

  3. \(2.3\)

  4. \(1.5\)

Question 2: Calculate \(E(Z^2)\)

Choose the correct answer:

  1. \(6.3\)

  2. \(1.01\)

  3. \(2.3\)

  4. \(1.5\)

Question 3: Calculate \(Var(Z)\)

Choose the correct answer:

  1. \(6.3\)

  2. \(1.01\)

  3. \(2.3\)

  4. \(1.5\)

Let \(X\) be a discrete random variable with \(E(X) = 1\) and \(Var(X) = 5\).

Question 4: What is \(E(2 + 3X)\)?

Choose the correct answer:

  1. \(6\)

  2. \(10\)

  3. \(45\)

  4. \(5\)

Question 5: What is \(E((2 + X)2)\)?

Choose the correct answer:

  1. \(6\)

  2. \(10\)

  3. \(45\)

  4. \(5\)

Question 6: What is \(Var(10 + 3X)\)?

Choose the correct answer:

  1. \(6\)

  2. \(10\)

  3. \(45\)

  4. \(5\)

Let \(Y\) be a discrete random variable with \(E(Y) = 4\) and \(Var(Y) = 2\). Remember, \(E(X) = 1\) and \(Var(X) = 5\) as above.

Question 7: What is \(E(21X - 4Y)\)?

Choose the correct solution:

  1. \(6\)

  2. \(10\)

  3. \(45\)

  4. \(5\)

Let \(Z_1\) and \(Z_2\) be discrete random variables. Suppose that \(Z_1\) and \(Z_2\) are independent.

\(E(Z_1) = 3\) and \(Var(Z_1) = 1\)

\(E(Z_2) = 5\) and \(Var(Z_2) = 2\)

Question 8: What is \(E(3 Z_1 - 2 Z_2 + 1)\)?

Choose the correct answer:

  1. \(0\)

  2. \(25\)

  3. \(17\)

  4. \(2\)

Question 9: What is \(Var(3 Z_1 - 2 Z_2 + 1)\)?

Choose the correct answer:

  1. \(0\)

  2. \(25\)

  3. \(17\)

  4. \(2\)

In a particular study, the percentage of the whole sample in groups defined by sex and smoking are shown below:

Sex

Current smoker

Former smoker

Never smoker

Male

10%

25%

15%

Female

20%

20%

10%

Question 10: What is the probability that a randomly selected individual is a current smoker?

Choose the correct answer:

  1. \(0.3\)

  2. \(1/3\)

  3. \(0.5\)

  4. \(1/5\)

Question 11: What is the probability that a randomly selected individual is male?

Choose the correct answer:

  1. \(0.3\)

  2. \(1/3\)

  3. \(0.5\)

  4. \(1/5\)

Question 12: Suppose we randomly select from among the male participants of the study. What is the probability that the selected individual is a current smoker?

Choose the correct answer:

  1. \(0.3\)

  2. \(1/3\)

  3. \(0.5\)

  4. \(1/5\)

Question 13: Suppose we randomly select from among the current smokers in the study. What is the probability that the selected individual is male?

Choose the correct answer:

  1. \(0.3\)

  2. \(1/3\)

  3. \(0.5\)

  4. \(1/5\)

Question 14: Are sex and smoking status independent variables?

Choose the correct answer:

  1. Yes

  2. No

  3. We do not have sufficient data to say

  4. No, because these events are not mutually exclusive

Quiz 6: Probability theorems Quiz 8: Continuous Random Variables