Probability As Relative Frequency Flashcards
When an experiment is performed a large. Umber of times, the relative frequency of an event……
Tends to be closer to the probability of the event.
Law of large numbers
Relative frequency
The proportion of times that an even happens
Number of times event happens/total number of trials
Nature of cumulative frequency graphs
Fluctuates at first then levels off
Complementary events
P(A^C)= 1- P(A)
Mutually exclusive events and Addition Rule
Cannot occur simultaneously, so:
P(A n B)= 0 and P(A u B)= P(A) + P(B)
General Addition rule (for events that are not mutually exclusive)
For any pair of events A and B,
P(A u B)= P(A) + P(B) - P(A n B)
Don’t add probabilities unless…
The events are mutually exclusive
Multiplication rule
The probability that BOTH events will occur is the product of their separate probabilities
Don’t multiply probabilities unless…
The events are independent
*independence is not the same as mutual exclusiveness
Conditional probability
Probability of an event given another event has occurred
P(A|B)= P(A n B)/P(B)
A and B are independent is P(A|B)=
P(A)
The only way two events can be mutually exclusive and independent
Id P(A)= 0 or P(B)= 0
Discrete numbers are associated with…
Countable numbers
Continuous numbers are associated with…
A whole line interval
A probability distribution for a discrete variable is….
A listing/formula giving the probability for each value of the random variable
Binomial probabilities
Applications on which a two-outcome stimulation
Repeated a certain number of times
The outcomes are independent
Probability of each of the two outcomes remains the same for each repetition
Binomial formula
(n) __n!___
(k) (p^k)(q^n-k)= k! (n-k)! (p^k)(q^n-k)
p= probability of success q= probability of failure n= number of trials k= number of successes
Phrases key for binomial distributions
At least
At most
Less than
More than
Geometric probability formula
(q^k-1)p
The probable that the first success is on trial number X= k
In performing a simulation, you must:
- Set up correspondence between outcomes and random numbers
- Give a procedure for choosing the random numbers (ex. Pick three fugues at a time from a designated row in a random number table)
- Give a stopping rule
- Note what is to be counted (what is the purpose of the simulation), and give the count if requested.
The expected value
The average or mean
The sums of ten products obtained by multiplying each value (xi) by the corresponding probability (pi)
E(X)= μx= Σ(xi)(pi)
If we have a binomial probability situation, with the probability of success equal to p and the number of trials equal to n, the expected value (mean) number of successes for the n trials is ____
np
Variance equation for a random variable X
σ^2= Σ(x-μ)^2(p)
Variance equation for a proportion
σ^2= np(1-p)
Law of Large numbers
States that in the long run, a cumulative relative frequency tends closer and closer to what is called the probability of an event
Shape of a histogram of a binomial distribution with p= .5
Is always symmetric
