Week 4

Question 1

What are Joint Distributions?

Answer 1

Multi-dimensional PDF (or PMF or CDF)

Question 2

What is the Joint PMF?

Answer 2

PX,Y(x, y) = P (X = x and Y = y)

Consists of an array of impulses.

Question 3

What is the Joint PDF?

Answer 3

P(A) = integrate fX,Y(x, y)dxdy

for any A C X(omega) x Y(omega).

Question 4

What is the Conditional PMF?

Answer 4

P X|A (xi) = P(X | xi = A) = P (X = xi and A) / P (A)

Question 5

What is Descriptive Statistics?

Answer 5

A summary that quantitatively describes features from a large collection of information, which does not assume that the data comes from a larger population.

Question 6

What are some common measures for descriptive statistics?

Answer 6

Central Tendency: Expectation (mean), median, mode etc.

Dispersion: Range and quartiles.

Spread: Variance and standard deviation.

Shape of the distribution: Skewness and kurtosi.

Question 7

What are the properties of variance?

Answer 7

Variance is the expectation of square minus the square of expectation.

Scale: Var(cX) = c^2Var(X)

Shift: Var(X + c) = Var(X)

If X and Y independent: Var(X + Y) = Var(X) + Var(Y)