# 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:

\(6.3\)

\(1.01\)

\(2.3\)

\(1.5\)

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

Choose the correct answer:

\(6.3\)

\(1.01\)

\(2.3\)

\(1.5\)

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

Choose the correct answer:

\(6.3\)

\(1.01\)

\(2.3\)

\(1.5\)

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:

\(6\)

\(10\)

\(45\)

\(5\)

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

Choose the correct answer:

\(6\)

\(10\)

\(45\)

\(5\)

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

Choose the correct answer:

\(6\)

\(10\)

\(45\)

\(5\)

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:

\(6\)

\(10\)

\(45\)

\(5\)

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:

\(0\)

\(25\)

\(17\)

\(2\)

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

Choose the correct answer:

\(0\)

\(25\)

\(17\)

\(2\)

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:

\(0.3\)

\(1/3\)

\(0.5\)

\(1/5\)

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

Choose the correct answer:

\(0.3\)

\(1/3\)

\(0.5\)

\(1/5\)

**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:

\(0.3\)

\(1/3\)

\(0.5\)

\(1/5\)

**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:

\(0.3\)

\(1/3\)

\(0.5\)

\(1/5\)

**Question 14**: Are sex and smoking status independent variables?

Choose the correct answer:

Yes

No

We do not have sufficient data to say

No, because these events are not mutually exclusive