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Random Variable
- Always numerical
- Represents the outcome of an experiment
- Can be discrete or continuous
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Are the number of discrete random values in an experiment infinite or finite?
Finite
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How long can a sequence be for a set of discrete random values?
Infinite
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Are the number of continuous random values in an experiment infinite or finite?
infinite
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What is the notation for a probability in a Discrete Probability Distribution?
f(x)
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Why aren't values in a graphical probability distribution connected like a histogram?
The values are discrete and there are no values in between
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What is the expected value of a discrete random value?
Mean
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What is the mean of a discrete random variable?
The value of x expected to occur in the long run and on average
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What is the Expected Value equation?
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What is the Variance of a Discrete RV equation?
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What is the Variance of a Discrete Random Variable (RV)?
Average squared deviations from the expected value
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What are examples of binomial results?
- 0 or 1
- Pass or Fail
- true or false
- success or failure
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Jakob Bernoulli was a contributor of what?
Calculus
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Jakob Bernoulli is known for what?
- Ars conjectandi - The art of conjecture
- First substantial treatise on probability
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What is ars conjectandi?
Contained theory of permutation and combination binomial theorem, multinomial theorum
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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
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In a Binomial Distribution, what is our interest?
The number of successes occurring in the n trials of a binomial experiment
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If you toss a coin 10 times, what is the probability of getting exactly 5 heads?
Let x = number of successes in n trials
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What is the binomial probability function?
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What does this part mean in the binomial probability function?
Number of outcomes providing exactly x successes in n trials
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What does this part mean in the binomial probability function?
Probability of a particular sequence of outcomes with x successes in n trials
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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
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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
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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
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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
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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
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What is the mean equation? (Expected value)
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What is the variance equation?
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What is the standard deviation equation?
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If you toss a coin 100 times, what is the expected value?
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If you toss a coin 100 times, what is the standard deviation?
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Of all small businesses, 27% are women-owned. In a sample of 200 small businesses, how many would you expect to be female-owned?
- n = 200, p = 0.27
 
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Of all small businesses, 27% are women-owned. if 8 small businesses were randomly selected, what is the probability that none are female-owned?
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Of all small businesses, 27% are women-owned. If 8 small businesses were randomly selected, what is the probability that half are female-owned?
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