Blue pages chapter 14-17
3.7(3)
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Last updated 4:21 AM on 1/6/23
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25 Terms
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probability
A number between O and 1 that reports the likelihood of that event's occurrence
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empirical probability
When the probability comes from the long-run relative frequency of the event's occurrence.
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probability rules
The probability of the entire sample space must equal 1.
The probability of an event occurring is 1 minus the probability that it doesn't occur.
The probability of an event occurring is 1 minus the probability that it doesn't occur.
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disjoint /mutually exclusive
Two events that share no outcomes in common. If A and B are disjoint, then knowing that A occurs tells us that B cannot occur.
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addition rule
If A and B are disjoint events, then the probability of A or B is
P(A UB) = P(A) + P(B).
P(A UB) = P(A) + P(B).
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multiplication rule
If A and B are independent events, then the probability of A and B is
P(AMB) = P(A) X P(B).
P(AMB) = P(A) X P(B).
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theoretical probability
When the probability comes from a model (such as equally likely outcomes).
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personal probability
When the probability is subjective and represents our personal degree of belief.
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general addition rule
For any two events, A and B, the probability of A or B is
P(AUB) = P(A) + P(B) - P(An B).
P(AUB) = P(A) + P(B) - P(An B).
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conditional probability
P(B|A)= P(A n B)/P(A)
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general multiplication rule
For any two events, A and B, the probability of A and B is
P(AnB) = P(A) X P(B |A).
P(AnB) = P(A) X P(B |A).
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Independence (equation)
Events A and B are independent when
P(B |A) = P(B).
P(B |A) = P(B).
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tree diagram
A display of conditional events or probabilities that is helpful in thinking through conditions
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random variable
a random variable assumes any of several different numeric values as a result of some random event. denoted with X
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discrete random variable
a random variable that can only take on the value of one number out of a finite amount of numbers
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continuous random variable
a random variable that can take on any numeric value within a range of values
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probability model
a probability model is a function that associates a probability P with each value of a discrete random variable X.
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expected value
The expected value of a random variable is its theoretical long-run average value, the center of its model.
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variance
the variance of a random variable is the expected value of the squared deviation from the mean.
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standard deviation
describes the spread in the model and is the square root of the variance.
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combining random variables
must look at variance to find the combined standard deviation. variance always ADDS
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multiplying by a constant
multiplies measures of center and location by b
multiplies measures of spread by |b|
widens/narrows the original shape
multiplies the variance by b^2
multiplies measures of spread by |b|
widens/narrows the original shape
multiplies the variance by b^2
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adding/subtracting by a constant
adds the constant to measures of center and location
does not change shape or spread
does not change shape or spread
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geometric probability model
used for a random variable that counts the number of trials before the first success
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binomial probability model
used for a random variable that counts the number of successes in a fixed number of trials.
