AP Stat Ch 5

Question 0

Probability

Answer 0

The probability of any outcome of a chance process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions

Question 1

Law of large numbers

Answer 1

Theorem in probability that describes the long term stability of a random variable. If we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value. We call this value the probability.

Question 2

Simulation

Answer 2

The imitation of chance behavior, based on a model that accurately reflects the phenomenon under consideration, is called a simulation

Question 3

Simulation steps

Answer 3

1. State the problem or describe the experiment
2. State the assumptions (heads and tails are equally likely and tosses are independent of each other)
   Assign digits to represent outcomes
3. Simulate many repetitions
4. State your conclusions

Question 4

Random

Answer 4

We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions

Question 5

Probability

Answer 5

The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. That is, probability is long term relative frequency.

Question 6

Sample space

Answer 6

Collection of all possible outcomes of a chance experiment

P(S)=1

Question 7

Multiplication principle

Answer 7

If you can do one task in n1 number of ways and a second task in n2 number of ways, then both tasks can be done in n1*n2 number of ways.

Question 8

Basic Rules of probability

Answer 8

Probability of an event must be between 0 and 1 (inclusive)
Sum of the probabilities of all possible outcomes must =1
If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities.
Complement principle

Question 9

Complement principle

Answer 9

P(A) + P(~A)=1

Question 10

Independent

Answer 10

When knowing that one event occurred will not change the probability of the second event. 
P(A|B) = P(A)
And P(B|A) = P(B)

Question 11

Disjoint events

Answer 11

Mutually exclusive events.

A and B cannot both happen. One or the other. P(A n B) = 0

Question 12

Addition rule

Answer 12

P(AUB) = P(A) + P(B) - P(AnB)

Question 13

Conditional probability

Answer 13

The notation P(A|B) is a conditional probability and is pronounced “The probability of A occurring given that B has already occurred.” It gives the probability of one event under the condition that we know another event.

Question 14

Multiplication rule for non independent events

Answer 14

P(A and B) = P(A) * P (B|A)

Question 15

Bayes’s Rule

Answer 15

States that conditional probability of event A given that B has occurred is:
P(A|B) = P(AnB) / P(B)

Question 16

Random variable

Answer 16

A random variable is a numerical variable whose value depends on the outcome of a chance experiment.

Question 17

Example of random variable

Answer 17

X= number of heads when you flip a coin three times.

Question 18

Discrete

Answer 18

A random variable is discrete if its set of possible values is a collection of isolated points on the number line. A discrete random variable, X, has a countable number of possible values.

Question 19

Continuous random variable

Answer 19

If its set of possible values includes an entire interval on the number line. The probability distribution of X is described by a density curve. Probability of any event is the area under the density curve and above the values of X that make up the event.

Question 20

Properties of density functions

Answer 20

Use area under density curve to get probability with continuous random variable.

1. F(x)>= 0
2. Total area under curve = 1
3. Probability X falls in any particular interval is = GO the area under the density curve in that interval.

Question 21

Mean of a random variable

Answer 21

Mean of a random variable X, mu, describes where the probability distribution of X is centered. Mean is an average of all possible values of X, but not all outcomes need to be equally likely.
A waited average. This is the expected value.