Probability As Relative Frequency

Question 0

When an experiment is performed a large. Umber of times, the relative frequency of an event……

Answer 0

Tends to be closer to the probability of the event.

Law of large numbers

Question 1

Relative frequency

Answer 1

The proportion of times that an even happens

Number of times event happens/total number of trials

Question 2

Nature of cumulative frequency graphs

Answer 2

Fluctuates at first then levels off

Question 3

Complementary events

Answer 3

P(A^C)= 1- P(A)

Question 4

Mutually exclusive events and Addition Rule

Answer 4

Cannot occur simultaneously, so:

P(A n B)= 0 and P(A u B)= P(A) + P(B)

Question 5

General Addition rule (for events that are not mutually exclusive)

Answer 5

For any pair of events A and B,

P(A u B)= P(A) + P(B) - P(A n B)

Question 6

Don’t add probabilities unless…

Answer 6

The events are mutually exclusive

Question 7

Multiplication rule

Answer 7

The probability that BOTH events will occur is the product of their separate probabilities

Question 8

Don’t multiply probabilities unless…

Answer 8

The events are independent

*independence is not the same as mutual exclusiveness

Question 9

Conditional probability

Answer 9

Probability of an event given another event has occurred

P(A|B)= P(A n B)/P(B)

Question 10

A and B are independent is P(A|B)=

Answer 10

P(A)

Question 11

The only way two events can be mutually exclusive and independent

Answer 11

Id P(A)= 0 or P(B)= 0

Question 12

Discrete numbers are associated with…

Answer 12

Countable numbers

Question 13

Continuous numbers are associated with…

Answer 13

A whole line interval

Question 14

A probability distribution for a discrete variable is….

Answer 14

A listing/formula giving the probability for each value of the random variable

Question 15

Binomial probabilities

Answer 15

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

Question 16

Binomial formula

Answer 16

(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

Question 17

Phrases key for binomial distributions

Answer 17

At least
At most
Less than
More than

Question 18

Geometric probability formula

Answer 18

(q^k-1)p

The probable that the first success is on trial number X= k

Question 19

In performing a simulation, you must:

Answer 19

1. Set up correspondence between outcomes and random numbers
2. Give a procedure for choosing the random numbers (ex. Pick three fugues at a time from a designated row in a random number table)
3. Give a stopping rule
4. Note what is to be counted (what is the purpose of the simulation), and give the count if requested.

Question 20

The expected value

Answer 20

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)

Question 21

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 ____

Answer 21

np

Question 22

Variance equation for a random variable X

Answer 22

σ^2= Σ(x-μ)^2(p)

Question 23

Variance equation for a proportion

Answer 23

σ^2= np(1-p)

Question 24

Law of Large numbers

Answer 24

States that in the long run, a cumulative relative frequency tends closer and closer to what is called the probability of an event

Question 25

Shape of a histogram of a binomial distribution with p= .5

Answer 25

Is always symmetric