Data Science and Machine Learning (Theory and Projects) A to Z - Expectations: Homework

The video tutorial explains a probability problem involving rolling a four-sided die three times. The focus is on determining the maximum roll, with the random variable having a uniform probability mass function. The tutorial guides viewers through calculating the expected value, variance, and fourth moment of the random variable. The session concludes with a homework assignment to apply these concepts.

What is the random variable of interest when rolling a four-sided die three times?

• The average of the rolls

• The sum of the rolls

• The minimum roll

• The maximum roll

If a random variable has a uniform PMF, what does it imply about the likelihood of its values?

• Values are not possible

• Values are inversely proportional

• All values are equally likely

• Some values are more likely than others

How do you calculate the expected value of a random variable with a uniform PMF?

• By finding the median of the values

• By averaging all possible values

• By summing the values

• By multiplying the values

What is the formula for calculating the variance of a random variable?

• Expected value of X squared

• Expected value of (X minus the mean) squared

• Expected value of X to the power of 4

• Expected value of X minus the mean

What does the fourth moment of a random variable represent?

• Expected value of X to the power of 5

• Expected value of X to the power of 4

• Expected value of X cubed

• Expected value of X squared