D3. Probability Density Function

Question 1

Define Proabability Density Function

Answer 1

Question 2

Attributes of PDFs

Answer 2

1. They are non-negative. f(x) ≥ 0
2. The sum of the area underneath the curve is equal to 1.

Question 3

Two important things to remember about PDFs

Answer 3

1. For continuous variables the probaility that X is observed to have exactly some value of x is zero: P(X=x) = 0
2. f(x) is not itself a probability

Question 4

What is the formula for the PDF of a uniform distribution over the interval {a,b}?

What does it look like?

Answer 4

Question 5

What does the PDF for the Normal look like? Attributes?

Answer 5

It is a bell curve f(x; μ, σ).

With parameters: μ - determining its location (mid-point), σ - determining its spread.