Module 4

Question 1

Probability Distribution Function (PDF)

Answer 1

Represents the likelihood of different outcomes in an experiment or study. For discrete variables, it specifies the probability of each possible outcome. For continuous variables, the PDF provides the probability density for each value, indicating the likelihood of a value falling within a particular range.

Question 2

Binomial Distribution

Answer 2

Can answer questions for variables that have or haven’t happened, defined by two parameters (number of trials, probability of success).

Question 3

What three things does a probability function capture

Answer 3

Shape: the general form or pattern of the distribution
Central tendency: what’s the average or expected value
Dispersion: how spread out or concentrated are the values around a typical value

Question 4

Cumulative Distribution Functions (CDF)

Answer 4

Give you the probability of getting a value less than or equal to X

Question 5

What three things are probability distributions good for

Answer 5

Simplyfing complexity - instead of dealing with vast datasets, you can summmarize data with a few parameters of a distribution

Predicting outcomes: with the known distribution and its parameters, public health officials can make informed predicitons

Flexible modeling: different distributions can be used to model different types of data, from the number of disease cases to the waiting times in a clinic

Question 6

Parameter

Answer 6

In relation to PDFs, a parameter refers to a numerical characteristic or constant that defines a specific aspect of the distribution. Parameters help describe the shape, spread, or central tendency of a distribution and remain constant for a given population, in contrast to sample statistics

Question 7

Expected Value

Answer 7

The expected value of a random variable represents the long-run average or mean value of the possible outcomes, when considering their probability. It is the weighted average of all possible values that the variable can take on, where each value is weighted by its probability of occurrence

Question 8

Binomial Distribution

Answer 8

Is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

Key parameters for a binomial distribution are n (number of trials) and p(probability of success on a single trial)

Question 9

Poisson Distribution

Answer 9

It is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space.

The key parameter for a Poisson distribution is Lambda, which represents the average number of occurrences in the interval

Question 10

When is a Poisson Distribution useful

Answer 10

1. Interval Independence: Events are independent of each other.
2. Rare Events: It’s especially useful when dealing with rare events.
3. Fixed Interval: The 􀆟me or space interval is fixed.
4. Average Rate: Events occur with a known constant mean rate.

Question 11

When is a binomial distribution useful

Answer 11

When there are 2 potential outcomes for each trial
When the probability of success is the same across all trials
When the number of trials is fixed
When each trial is independent