Class 3 Notes Questions

Question 1

What are random variables?

Answer 1

Most variables are random in the sense that we can’t predict their exact values from one value to the next.
Upper-case variables like 𝑋 refer to the whole random variable,
whereas lower-case variables like 𝑥 refer to values of 𝑋.

Question 2

What are 𝜇? 𝜎? x̄? s? 𝜎x̄?

Answer 2

𝜇: population mean
𝜎: population standard deviation
x̄: sample mean
s: sample standard deviation
𝜎x̄: sample standard error

Question 3

example of theoretical probability distribution to frequency distribution

Answer 3

sum of two dice with the “Freq. Dist. 10,000 Dice Rolls” graph matching the “Prob. Dist. (Theory)” graph

Question 4

What is the Bernoulli Distribution? And an example.

Answer 4

Data with a Bernoulli distribution take on the discrete, binary values of 0 or 1.
For example, a flip of a fair coin provides one example of an random event that follows a Bernoulli distribution. That is the case because a flip of a fair coin has only two outcomes:

Heads (1) or Tails (0).
Assuming that the coin is truly fair, the probability of obtaining either Heads or Tails is 0.5. People usually assign the probability of obtaining Heads as 𝑝 and Tails as 1 − 𝑝

Question 5

What is a histogram? And an example.

Answer 5

Histograms capture the number of observations within specific intervals/ ranges that are called bins. Narrower bins provide more detail than wider bins, but the choice of bin size depends on the problem at hand.

F D C B A
Grade
F D− D D+C− C C+B− B B+A− A A+
Grade

Question 6

Histogram vs. Bar graph

Answer 6

Histogram
- Distribution of non-categorical data
- Each bin shows a group of observations
- Bin order is important

Bar graph
- Count of categorical or binary data
- Each bar represents one category of data
- Bin order is arbitrary

Question 7

What is a Q-Q plot? Specifically of Simulated Normal Data

Answer 7

The Q-Q plot assesses how much sample quantities look like theoretical quantities from a normal distribution. The Q-Q plot achieves that by dividing the data into smaller, equally-sized intervals/subsets called quantiles

Below is an example Q-Q plot. Most of the data hang close to the 45-degree line,
indicating that the sample data resemble a normal distribution.

Question 8

What is skewness?

Answer 8

Skewness measures the asymmetry of a distribution. It indicates the extent to which a distribution leans to the left (negative skew) or to the right (positive skew).

Question 9

What is kurtosis?

Answer 9

Kurtosis measures the “tailedness” or the peakedness of a distribution. It indicates how heavy or light the tails of the distribution are compared to a normal distribution. The high kurtosis distribution is more pointy, whereas
the normal distribution is more bell-shaped.