C3_W2_Quiz.md

1. What is the expected value of rolling a fair six-sided dice?

• $1$
• $3.5$
• $3$
• $6$

2. If we roll two fair six-sided dice, what is the probability that the sum of the dice is greater than or equal to 9?

• $1/9$
• $1/6$
• $5/18$
• $1/3$

3. The box plot bellow shows the distribution of salaries for employees in three different departments of a company. Interpret the box plot and select all that apply.

• The median salary of department 2 is higher than the median salary of department 1.
• The IQR of department 3 is smaller than department 1.
• There are no outliers in depertment 2.
• The range of salaries in department 3 is larger than the range of salaries in depertment 2.

4. Which of the following QQ plots represents a set of data that is more likely normally distributed?

• (A)

• (B)

• (C)

• (D)

5. A fair six-sided dice is rolled. What is the expected value of the square of the number rolled?

• (A)

$$\frac{7}{6}$$

• (B)

$$\frac{35}{36}$$

• (C)

$$\frac{91}{6}$$

• (D)

$$\frac{49}{36}$$

6. Suppose that the joint probability distribution of two random variables X and Y is given by the following table:

$$\begin{matrix} \text{X/Y} & | & 1 & 2 & 3 \cr \hline 1 & | & 0.1 & 0.2 & 0.3 \cr 2 & | & 0.2 & 0.1 & 0.1 \end{matrix}$$

What is the probability that X and Y both take even values?

• $0.2$
• $0.1$
• $0.3$
• $0.4$

7. About the correlation coeficient, it is correct to say (check all that apply):

• It is always positive real number.
• It can be any real number.
• It measures how linearly correlated two variables are.
• It is a real number between -1 and 1.

8. Suppose that the joint probability distribution of two random variables X and Y is given by the following table:

$$\begin{matrix} \text{X/Y} & | & 0 & 1 \cr \hline 0 & | & 0.2 & 0.1 \cr 1 & | & 0.1 & 0.6 \end{matrix}$$

What is the covariance between X and Y?

• $-0.04$
• $0.11$
• $0.02$
• $0.04$