Chapter 4&5 Flashcards
The ________ of a discrete random variable represents the mean value of the outcomes
expected value
The ________ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further
Sample space
The classical approach to probability requires that the outcomes are _______.
Equally likely
As a procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as ____________________.
The law of large numbers
Principles of probability
- The probability of an event is between 0 and 1 inclusive
- The probability of an event certain to occur is 1
- The probability of an impossible event is 0
Classical approach to probability (equally likely outcomes)
P(A) = number of ways A occurs/number of different simple events = s/n
Relative frequency approach of probability (observe and count)
P(A) = # of times A occurs/ # of times procedure repeated
Subjective Probability
P(A) is estimated
Simulation
Process that behaves in the same ways as the procedure itself so that similar results are produced
Complement
Consists of all outcomes in which event A does not occur
Significantly high number of successes
Probability of 0.05 or less
Disjoint events
Two events cannot occur at the same time
Drive thru ?
- Add all orders to get total
- Add all accurate orders
- Add accurate order total to not accurate number from restaurant A = x
- Take x and divide by total
At least one is equivalent to __________.
“One or more”
A ________ probability of an event is a probability obtained with knowledge that some other event has already occurred.
Conditional
Confusion of the inverse occurs when we incorrectly believe ___________.
P(B|A) = P(A|B)
Multiplication Rule
P(A and B) = P(A) • P(B|A)
Independent events
(Replacement)
Dependent events
(No replacement)
Tested positive| given no disease
- Add all no disease
- positive test(no disease)/ individual no disease
Permutations
Order matters
- n different items are available and r of them are selected without replacement
Combinations
Order does not matter
Multiplication rule
P(A and B) = P(A) • P(B|A)
Combination lock
Uses multiplication rule
A _________variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
Random
A ___________random variable has either a finite of a countable number of values.
Discrete
A ____________ random variable has infinitely many values associated with measurements.
Continuous
In a probability histogram, there is a correspondence between __________.
Area and probability
The ________ of a discrete random variable represents the mean value of the outcomes.
Expected value
Random variable
Variable with a single numerical value, determined by chance, for each outcome of a procedure.
Probability distribution
- Between 0 and 1
- All values added to 1
- Values must be numerical
Binomial Probability Requirements
- Fixed number of trials
- 2 possible outcomes, success and failure
- Probability of success remains the same in all trials
- Trials are independent
In the binomial probability formula, the variable x represents the __________.
Number of successes
