Chapter 5: Doscrete probaility Distributions

Question 1

Random variable

Answer 1

-represents a numerical value associated with each outcome of a probability distribution
-denoted by x

Question 2

direct random variable

Answer 2

-has a finite or countable number of possible outcomes that can be listed

Question 3

continuous random variable

Answer 3

-has an uncountable number of possible outcomes, represented by an interval on the number line

Question 4

discrete probability distribution

Answer 4

-list each possible value the random variable can assume, together with its probability
-must satisfy:
1. the probability of each value of the discrete random variable is between 0 and 1, inclusive
2. the sum of all the probabilities is 1

Question 5

How to create a discrete probability distribution

Answer 5

1. make a frequency distribution for the possible outcomes
2. find the sum of the frequencies
3. find the probability of each possible outcome by dividing its frequency by the sum of the frequencies
4. check that each probability is between 0 and 1 and that the sum is 1

Question 6

the expected value of a discrete random variable

Answer 6

-is equal to the mean of the random variable

Question 7

binomial experiments

Answer 7

-the experiment is repeated for a fixed number of trials. where each trial is independent of other trials
- there are only two possible outcomes of interest for each trial. The outcomes can be classified as success or a failure
-the probability of success is the same for each trial
- the random variable x counts the number of successful trials