Module 3

Question 1

What’s a random variable?

Answer 1

• Numerical description of the outcome of an experiment
• Can be either discrete or continuous

Question 2

What’s a discrete random variable?

Answer 2

Can be either a finite number of values or an infinite sequence.
There’s discrete values the variable can take, for instance the value of rolling two dice won’t have any decimal points - it’s only whole numbers.

Question 3

What’s a continuous random variable?

Answer 3

Could take any value in the line of possible values (for example instead of only being able to be a whole number, it could be literally any number with any number of decimal points within a certain range)

Question 4

What’s an Empirical Discrete Distribution?

Answer 4

Discrete probability distribution based on the relative frequency method of assigning probabilities.

Question 5

What are the conditions for a Discrete Probability Function?

Answer 5

Sum of all f(x) = 1
(0</= f(x) </= 1)

Question 6

Do you get a line graph with a discrete probability function?

Answer 6

NO! You just get the individual dots because they’re discrete.

Question 7

What’s the Bernoulli Process?

Answer 7

1. Two outcomes are possible on each trial. We refer to one outcome as a success and the other outcome as a failure.
2. Stationary Assumption: The probability of a success, denoted by p, does not change from trial to trial. Consequently, the probability of a failure, denoted by 1–p, does not change from trial to trial.
3. The trials are independent.

Question 8

What’s a Binomial Experiment?

Answer 8

• The experiment consists of a sequence of n identical trials.
• Plus: Bernoulli Process
• X is a discrete random variable

Question 9

What are the basics of a Poisson Probability Distribution?

Answer 9

• Discrete random variable
• No stated upper limit of x
• For estimating the # of occurrences over a specified interval (time or space).
• The mean & the variance of the distribution are equal
• Rules:
  The probability of an occurrence is the same for any two intervals of equal length
  The (non)occurrence in any interval is independent of the (non)occurrence in any other interval.
  If you’re trying to find the probability of something without being given SD, it’s probably a Poisson distribution, because you don’t need a z-score for the table, just mu and x.

Question 10

What are the basics of a Hypergeometric Probability Distribution?

Answer 10

• Trials are not independent
• Probability of success changes from trial to trial
• Sampling is done without replacement

Question 11

What are the basics of Bivariate or Joint Empirical Discrete Probability Distributions & Covariance?

Answer 11

• Two random variables
• Covariance of Random Variables X & Y

Question 12

How do we create a probability distribution?

Answer 12

• Table containing all the values that can happen based on the probability table they’ve given you, and what the probability of those values is.
• lists E(x) and SD
• Don’t forget column totals! (or row totals if you’re using columns)