Chapter 5: Discrete Probability Distributions

Random Variable

A variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure.

Probability distribution

A description that gives the probability for each value of the random variable. It is often expressed in the format of a table, formula, or graph.

Discrete Random Variable

A collection of values that is finite or countable. (If there are infinitely many values, the number of values is countable if it is possible to count them individually, such as the number of tosses of a coin before getting heads.)

Continuous random variable

Has infinitely many values, and the collection of values is not countable. (That is, it is impossible to count the individual items because at least some of them are on a continuous scale, such as body temperatures.)

Expected value of a discrete random variable

Denoted by E, and it is the mean value of the outcomes,

What are the requirements of a probability distribution?

1. There is a numerical random variable x, and its numerical values are associated with corresponding probabilities.

2. The sum of all probabilities must be 1, sums such as 0.999 or 1.001 are acceptable.

3. Each probability value must be between 0 and 1 inclusive.

Mean of probability distribution

Sum of x*(it’s corresponding probability)

Binomial probability distribution

A procedure that has

1. Fixed number of trials.

   2. Independent trials.

   3. Two outcomes

   4. The probability of a success is the same