Chapter 5: Discrete Probability Distribution

Random Variables may be classified as:

- Discrete: the random variables assumes a countable number of distinct values. - Continuous: the random variable is characterized by (infinitely) uncountable values within any interval.

Every Random variable is...

- associated with a probability distribution that describes the variable completely.

T/F: A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcome and the probabilities of each outcome remain the same.

False

T/F: A cumulative probability distribution of a random variable X is the probability P(X=x), where X is equal to a particular value x.

False

T/F: The variance of a random variable X provides us with a measure of central location of the distribution of X.

False

An Excel's function ____________ is used for calculating Poisson probabilities.

POISSON.DIST

T/F: The expected value of a random variable X can be referred to as the population mean.

True

Random Variable

a function that assigns numerical values to the outcomes of an experiment. - Denoted by uppercase letters (e.g., X) - Values of the random variable are denoted by corresponding lowercase letters.

Which of the following can be represented by a discrete random variable? a) The number of obtained spots when rolling a six-sided die b) The height of college students c) The average outside temperature taken every day for two weeks d) The finishing time of participants in a cross-country meet

a) The number of obtained spots when rolling a six-sided die

What is a characteristic of the mass function of a discrete random variable X? a) The sum of probabilities P(X=x) over all possible values x is 1. b) For every possible value x, the probability P(x=x) is between 0 and 1. c) Describes all possible values x with the associated probabilities P(X=x). d) All of the above.

d) All of the above.

cumulative distribution function

may be used to describe either discrete or continuous random variables.

We can think of the expected value of a random variable X as:

the long-run average of the random variable values generated infinitely many independent repetitions.

Probability density function

used to describe continuous random variables.

Probability mass function

used to describe discrete random variable.