Statistics Exam 2

Question 1

Variables that vary within their domain and depend on the outcome of an experiment.

Answer 1

Random Variables

Question 2

Type of distribution that has only two outcomes.

Answer 2

Bernoulli Distribution

Question 3

Defines the “Shape” of a distribution

Answer 3

Parameter

Question 4

Seeks to determine the probability that something is less than or equal to a number or greater than or equal to a number.

Answer 4

Cumulative Distribution Function (CDF)

Question 5

The value you would most likely expect for an outcome given a pmf.

Answer 5

Expected Value

Question 6

Describes the spread of the values of the sample in the population.

Answer 6

Variance of a Random Variable

Question 7

Assumptions:
1. Each trial has two possible outcomes.
2. The trials are independent.
3. On each trial, the probability of success is P and failure is 1-p.

Answer 7

Bernoulli, Geometric, and Binomial Distributions

Question 8

Applications:
- Tossing of a coin.
- Lights on or off.
- Disease in a person.
- Roulette wheel.

Answer 8

Bernoulli Distribution

Question 9

Applications:
- The first success occurring on the Xth trial.
- The number of failures before the first success.

Answer 9

Geometric Distribution

Question 10

The sum of N Bernoulli trials.

Answer 10

Binomial Distribution

Question 11

Applications:
- Six heads when you toss a coin ten times.
- 12 women in sample size of 20.
- Three defective items in batch of 100.

Answer 11

Binomial Distribution

Question 12

Assumptions:
1. There is a finite population of size N.
2. Each trial has two possible outcomes (success / failure) and there are M successes in the population.
3. A sample size of n is selected without replacement.

Answer 12

Hypergeometric Distribution

Question 13

Applications:
- The Powerball lottery.
- Poker hands.
- Chance of picking a defective part from a box.
- Picking R or D voters in a sample of voters in a district.

Answer 13

Hypergeometric Distribution

Question 14

Assumptions:
1. Each trial has two possible outcomes (success / failure).
2. The trials are independent.
3. On each trial, the probability of success is p and failure is 1-p.

Answer 14

Negative Binomial Distribution

Question 15

Applications:
- Rolling the 5th 6 on the 20th roll of a die.
- Getting the 10th defective item on the 1000th item inspected.
- Selecting the 10th woman as the 15th participant .

Answer 15

Negative Binomial Distribution

Question 16

Assumptions:
1. The data are counts of events.
2. All events are independent.
3. The average rate of occurrence does not change during the period of interest.

Answer 16

Poisson Distribution

Question 17

Applications:
- Text messages per hour.
- Customers in a restaurant.
- Machine malfunctions.
- Website visitors per month.

Answer 17

Poisson Distribution

Question 18

Variables that vary within their domain (the sample space), can take on any value in a range, and depend on the outcome of an experiment.

Answer 18

Continuous Random Variables

Question 19

Distributions that are countable, have distinct points, the points have probability, and p(x) is a probability mass function.

Answer 19

Discrete Distributions

Question 20

Distributions that are uncountable, are on a continuous interval, the points have no probability, and f(x) is a probability density function.

Answer 20

Continuous Distributions

Question 21

Assumptions:
1. All outcomes have an equally likelihood of occurrence.
2. All values have a constant probability.
3. Symmetric data.

Answer 21

Uniform Distribution

Question 22

Applications:
- Random number generator.
- Random sampling.
- Radioactive decay over time.

Answer 22

Uniform Distribution

Question 23

Assumptions:
1. Symmetric data.
2. The mean, median, and mode are all equal.
3. Half the population is less than the mean and half is greater than the mean.

Answer 23

Normal Distribution

Question 24

Applications:
- Heights of individuals.
- Blood pressure.
- IQ scores.
- Measurement errors.

Answer 24

Normal Distribution

Question 25

Assumptions:
1. Deals with time until an event.
2. Important property that is the distribution is memoryless.
3. Often seen as the inverse of the Poisson parameter.

Answer 25

Exponential Distribution

Question 26

Applications:
- Time until a bus arrives.
- Time until the 3rd customer enters.
- Days before travel that a ticket is purchased.

Answer 26

Exponential Distribution

Question 27

Assumptions:
1. Intervals over which the events occur do not overlap.
2. The events are independent.
3. The probability that more than one event happens in a very short time period is approx. zero.

Answer 27

Gamma Distribution

Question 28

Applications:
- Time between independent events.
- Time until death.
- Time until parts wear out.
- Time until the 3rd accident.

Answer 28

Gamma Distribution

Question 29

Specifies the number of events you are modeling.

Answer 29

Shape Parameter (Gamma Distribution)

Question 30

Represents the mean time between events.

Answer 30

Scale Parameter (Gamma Distribution)

Question 31

Assumptions:
1. Data is independent.
2. Identically distributed.

Answer 31

Weibull Distribution

Question 32

Applications:
- Widely used in reliability.
- Fits a wide variety of data sets allowing for both left and right skewed data.

Answer 32

Weibull Distribution

Question 33

Assumptions:
1. The logarithm of the RV is distributed normally.
2. Same as Normal distribution.

Answer 33

Lognormal Distribution

Question 34

Applications:
- Milk production by cows.
- Lives of industrial units with failure modes.
- Amount of rainfall.
- Size of raindrops.

Answer 34

Lognormal Distribution

Question 35

Applications:
- Used if there is a finite interval for the RV X.

Answer 35

Beta Distribution

Question 36

Whether a variation in one variable results in a variation of another.

Answer 36

Covariance

Question 37

The direction and the strength of the relationship between two variables.

Answer 37

Correlation

Question 38

Type of probability distribution that is created by drawing many random samples of the given size from the same population.

Answer 38

Sampling