Stats exam 2

What is true about the general rule of addition

if the events a and b are not mutually exclusive, you can use it. (works for all, must be used here)

What is an example of subjective probability?

if you apply for a job after graduation, your chance of getting the job is 83%

benefit of the continuity correction factor

it allows for the approximate calculation of a discrete probability from a continuous distribution

"Family" of normal distribution means

1. distributions may have different means and standard deviations but still be normal in shape 2. a single equation describes all normal distributions

What is true about the special rule of addition

If the events A and B are mutually exclusive, you can use it.

Special rule of multiplication formula

P(A and B) = P(A)P(B)

Equation for P(A or B)

P(A) + P(B) - P(A and B)

Exponential Distribution equation

P(x)= Lamdae^-lamda*x

Poisson Distribution

The intervals do not overlap and are independent The probability of the vent is proportional to the interval size The random variable is the number of occurrences during an interval

a random variable can be defined as

a quantity resulting from a random experiment that can have different values

in the context of Baye's theorem, what is Posterior probability

a revised probability based on additional information

Identical prizes are given to two winner from a group of 12 contestants. What counting formula would you use to determine how many ways the prizes could be given out?

combination formula

A table used to classify observation according to two or more identifiable characteristics, and often used to determine probabilities is called a ________ table?

contingency

What is the name of the table that shows the relationship between two variables

contingency table

What describes the relationship between the Poisson distribution and the binomial distribution?

it is a limiting form of the binomial distribution when the probability of success is very small and the sample is very large

variance of binomial distribution

npi(1-pi)

standard deviation when uniform distribution, min=a, max=b,

sqrt((b-a)^2 /12)

Exponential Distribution

the events occur independently and at a constant rate per unit of time length

How is empirical probability calculated

the number of times the vent occurs divided by the total number of observations

features of a binomial experiment

the probability of sucess stays the same for each trial the random variable counts the number of successes in a fixed number of trials

mean of a binomial distribution

u=npi

subjective probability

weighing the available information and assigning a probability.

when can a binomial distribution be used as a good approximation to a hypergeometric distribution

when the sample size is less than 5% of the population, meaning the samples are almost independent

3 characteristics of exponential distribution

1. it is characterized by only one parameter, known as the rate parameter 2. the random variable is always positive 3. The distribution is asymmetrical and positively skewed

Purpose of converting a random variable to a z-value

1. to express the distance from the mean in terms of the standard deviation 2. to compare a normal distribution to a standard normal distribution

uniform distribution of x when a<x<b

1/(b-a)

What does it mean for something to be collectively exhaustive?

An event has to occur