Stats: Probability Ch.4

When did statistics get so difficult for me ðŸ˜¦ Long time no number….

Ch. 4 Summary : Probability and Probability Distribution

4.1: main role is to turn sample values into population values…

4.2:
EXPERIMENT: the process
SIMPLE EVENT: outcome observed from single repetition of the experiment
EVENT: collection of simple events
MUTUALLY EXCLUSIVE: when one event occurs, the other cannot, v/v
SAMPLE SPACE (S): set of all simple events

4.3:
PROBABILITY OF EVENT A: when n approaches infinite, frequency divided by n. it is equal to the sum of the probabilities of the simple events contained in A.
– probability lies between 0 and 1
– probability of all simple events adds to 1
So, how to CALCULATE probability of an event?
1. list all the simple events in the sample space
2. assign an appropriate probability to each simple event
3. Determine which simple events result in the event of interest
4. Sum the probabilities of the simple events that result in the event of interest

4.4: Since it’s an “optional” section … let me skip hehe

4.5: Event Relations and Probability Rules (Love this section)
UNION: either/or
INTERSECTION: both
COMPLEMENT: when A does NOT occur! everything other than A.
ADDITION RULE: P(A union B) = P(A) + P(B) – P(A intersection B)
P(A intersection B) is 0 when A and B are mutually exclusive, of course
P (complement of A) is 1-P(A)

4.6:
INDEPENDENT: if and only if P(B) is not influenced or changed by the occurrence of event A, vice versa.
P(A|B): conditional probability of A, given that B has occurred.
GENERAL MULTIPLICATION RULE: P(A intersection B)= P(A)P(B|A) or P(B)P(A|B)
****?????CONDITIONAL PROBABILITIES???? ME DOES NOT GET SOME EQUATIONS:(
Need to know the difference between mutually exclusive and independent events~!

4.7: Also optional… ðŸ™‚ hehe…;;;

4.8:
RANDOM VARIABLE x: by chance
PROBABILITY DISTRIBUTION: for a discrete random variable is… formula, table, graph… that gives possible values of x, and the probability p(x) associated with each value of x!
EXPECTED VALUE:
VARIANCE of x:
STANDARD DEVIATION OF A RANDOM VARIABLE x: