EXAM 2-Ch. 3 (2/29) Flashcards
probability
a value between 0 and 1, inclusive [0,1], describing the relative chance an event will occur
probability that an event will occur=
number of ways the event can occur/total number of possible outcomes
rules of probability:
- prob. must be a positive real number between 0 and 1
- prob. of 1 means the event is certain to occur (like saying 100%) and prob. of 0 means the event is certain NOT to occur
- addition rule
- compliment rule
- multiplication rule
- conditional probability
addition rule:
If A and B are mutually exclusive events, then P (A or B)=P (A) + P(B)-P(A and B)
*mutually exclusive=both events can’t happen at the same time
compliment rule:
a “compliment” is defined as all events NOT included in event A
P(A)=P(A’)+1 OR P(A)=1-P(A’)
multiplication rule:
If A and B are independent events, then P(A and B)=P(A) x P(B)
*independent events=the occurence of one event DOES NOT affect the probability of occurence of another event
conditional probability:
P(A/B)=P(A and B)/P(B) OR P(A and B)=P(A/b) x P(B)
*P(A/B) is read as: “prob. of A given B”
combinations equation
C ( n!/x! (n-x)!)
n x
probability distribution:
a listing of all the possible values a random variable can assume along with the probabilities of obtaining those values
can be as tables, formulas, or graphs
for a discrete random variable x
to be a valid prob. distribution:
- 0 ≤ P(x sub c) ≤ 1, for each x
- sum of P(x)=1
for a discrete random variable x
population mean:
μ=E(X)=(sum of x) x p(x)
μ= “mu”, E(x)=”expected value of x” aka long run average
basically just a weighted mean across all the possible values of x
for a discrete random variable x
population variance=
sum x sqaured x p(x)-μ squared
for a discrete random variable x
standard deviation=
σ=s(x)=square root 1/2
a binomial probability distribution is
a common discrete probability distribution
rules of a binomial experiment:
- consists of a fixed number of trials, n
- each trial has only 2 possible outcomes (success/failure)
- P(success)=π ( a symbol, not actual pi)= 1-π
- trials are independent, which means the outcome of one trial does nto affect the outcome of another trial (probability of success remains constant from trial to trial) *think: 50% of success will stay the same for heads or tails!
the binomial random variable (x):
the number of successes in “n” trails. It takes on the values 0,1,2….n
x=# of successes
to calculate the probabilities of “x” successes in “n” trials in a binomial experiment w/ probability of success, “π” use the equation:
p(x)=C π raised to the x (1-π) raised to
n x n-x
for a binomial random variable:
μ=nπ
σ squared=nπ(1-π)
σ=square root nπ(1-π)
normal probability distributions are:
-bell-shaped
-mean=median=mode
-symmetrical about the mean
-asymptotic to the x-axis (limit)
-location determined by μ and σ
we can find probabilities for any normally distributed random variable by
using the standard normal distribution (aka z-distribution)
z distribution
a normal distribution with μ=0 and σ=1
standard normal random variable (z score):
Z= x-μ/σ
basically putting the data in standard deviation units
tells us how many standard deviations a value is from the mean
z scores above the mean
will always be positive
z scores below the mean
will always be negative
