MATH2224202 Probability & Statistics

A joint pmf can contain negative values if the sum of all probabilities equals 1.

P(A∣B)=P(A)/P(B)​ for any events A and B.

The marginal probability P_X(x) can be greater than any joint probability P(X=x,Y=y).

If X and Y are independent, then Var(X+Y)=Var(X)+Var(Y).

Mutually exclusive events are always independent.

If events A and B are mutually exclusive, then P(A∪B)=P(A)+P(B).

The sum of probabilities in a discrete probability distribution can be greater than 1 if the variable has many values.

If P(X=x, Y=y)=P_X(x)⋅P_Y(y) for some values of x,y, then X and Y are independent.

If X and Y are independent, then E[XY]=E[X].

The probability of an event is always between −1 and 1.

The cumulative distribution function (CDF) of a discrete random variable is always a non-decreasing function.

The number of ways to choose 3 elements from a set of 5 without replacement is 10.

E[X+Y]=E[X]+E[Y] only if X and Y are independent.

The expected value of a discrete random variable is the weighted average of its possible values.

You can apply Bayes’ Rule without knowing P(B) as long as you know P(B∣A) and P(A).