Statistics Chapter 5  Discrete Random Variables
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Random Variable
 Always numerical
 Represents the outcome of an experiment
 Can be discrete or continuous

Are the number of discrete random values in an experiment infinite or finite?
Finite

How long can a sequence be for a set of discrete random values?
Infinite

Are the number of continuous random values in an experiment infinite or finite?
infinite

What is the notation for a probability in a Discrete Probability Distribution?
f(x)

Why aren't values in a graphical probability distribution connected like a histogram?
The values are discrete and there are no values in between

What is the expected value of a discrete random value?
Mean

What is the mean of a discrete random variable?
The value of x expected to occur in the long run and on average

What is the Expected Value equation?

What is the Variance of a Discrete RV equation?

What is the Variance of a Discrete Random Variable (RV)?
Average squared deviations from the expected value

What are examples of binomial results?
 0 or 1
 Pass or Fail
 true or false
 success or failure

Jakob Bernoulli was a contributor of what?
Calculus

Jakob Bernoulli is known for what?
 Ars conjectandi  The art of conjecture
 First substantial treatise on probability

What is ars conjectandi?
Contained theory of permutation and combination binomial theorem, multinomial theorum

What are the 4 properties of a binomial experiment?
 There are n identical trials in a series
 Each trial has two mutually exclusive outcomes (heat/tails, success/failure)
 Probability of success p, is constant from trial to trial
 Outcomes are independent

In a Binomial Distribution, what is our interest?
The number of successes occurring in the n trials of a binomial experiment

If you toss a coin 10 times, what is the probability of getting exactly 5 heads?
Let x = number of successes in n trials

What is the binomial probability function?

What does this part mean in the binomial probability function?
Number of outcomes providing exactly x successes in n trials

What does this part mean in the binomial probability function?
Probability of a particular sequence of outcomes with x successes in n trials

What can you say about a binomial distribution with the following variables?
n = 5
p = 0.1
 The highest success rate would be 0
 The lowest success rate would be 5
 The graph is skewed right

What can you say about a binomial distribution with the following variables?
n = 5
p = 0.5
 The highest success values would be 2 and 3 (midpoint between 0 and 5)
 The lowest success values would be 0 and 5
 The graph is normally distributed

What can you say about a binomial distribution with the following variables?
n = 5
p = 0.9
 The success value would be 5
 The lowest success value would be 0
 The graph is skewed left

What can you say about a binomial distribution with the following variables?
n = 20
p = 0.2
 The highest success values are 3 and 4
 The lowest success values are 11  20
 The graph is highly skewed right

What can you say about a binomial distribution with the following variables?
n = 50
p = 0.5
 The highest success values would be around 25
 The lowest success values would be going out from that towards the edges
 The graph is a normal distribution

What is the mean equation? (Expected value)

What is the variance equation?

What is the standard deviation equation?

If you toss a coin 100 times, what is the expected value?

If you toss a coin 100 times, what is the standard deviation?

Of all small businesses, 27% are womenowned. In a sample of 200 small businesses, how many would you expect to be femaleowned?
 n = 200, p = 0.27

Of all small businesses, 27% are womenowned. if 8 small businesses were randomly selected, what is the probability that none are femaleowned?

Of all small businesses, 27% are womenowned. If 8 small businesses were randomly selected, what is the probability that half are femaleowned?