ALL UNIT 4 Flashcards
major difference between bino and geo?
BINO is about a number of successes
GEO is all about when the FIRST SUCCESS happens
what is the big difference between PDF and CDF?
The PDF’s are EXACTLY,
so exactly 5 successes (binopdf),
or first success exactly on the seventh try (geopdf).
CDF’s are CUMULATIVE (added up),
so 5 OR LESS successes (binocdf)
or the first success ON OR BEFORE the seventh try (geocdf)
binocdf vs geocdf
both cumulative
(added up probabilities)
binocdf tells you P(X OR LESS successes… )
geocdf tells you P(First success ON OR BEFORE…. )
binocdf vs binopdf
cdf is cumulative
it tells you “x or less successes”
pdf is not
it tells you “exactly x successes”
geocdf vs geopdf
geocdf is cumulative
it tells you “first success ON OR BEFORE the xth try”
geocdf is exact
it tells you “first success exactly ON the xth try”
binopdf vs geopdf
both are pdf
(both not cumulative)
binopdf tells P(EXACTLY X successes)
geopdf tells P(FIRST SUCCESS ON… )
binopdf
binocdf
geopdf
geopdf
binopdf: EXACTLY x successes in N tries
binocdf: X OR LESS successes in N tries
geopdf: FIRST SUCCESS on the xth try
geocdf: FIRST SUCCESS ON OR BEFORE the xth try
Give three examples of independent variables
- Being tall and having a high GPA
- If it is snowing and whether it is a Thursday or not
- Whether a person likes pizza and their gender
(notice, knowing one bit of information does not impact the likelihood of the other being true also)
When to use general mult rule and what is it?
AND probability.
Use when associated.
P(this)*P(that|this).
IT ALWAYS WORKS FOR ALL SITUATIONS. When indep, the P(that|this) = P(that). So you end up with the simpler independent version: P(this)*P(that)
If combining 4 random variables with standard deviations of m, p, q, r….
What is the new combined standard deviation?
SQRT(m2 + p2 + q2 + r2)
RAND VARIABLE:
X has mean y and standard deviation of z.
A has mean b and standard deviation c.
Find: Mean, SD and VAR of: X + X + X
mean: y+y+y
sd: SQRT(z2+z2+z2) ….
var: (z2+z2+z2)
what is independence?
What are the two equations to test for independence?
when P(A)=P(A|B) OR P(A)*P(B)=P(A and B)
When the probability of A is the same even when B is also true.
Knowing B does not affect the probability of A.
what does geometric model tell us about?
THE FIRST SUCCESS
Like, what is likelihood first success is on 5th trial?
What is the area under the normal curve?
1 or 100%
The area under any probability curve is 1.00
How many ways can I arrange 4 letters?
4!
4*3*2*1= 24 ways
Give three examples of variables that are not independent (associated)
- Playing video games and gender (Knowing male makes it more likely they play)
- Whether it is snowing and the month you are in (some months are more rainy than others, knowing what month changes likelihood of snowing)
3 If a pet is a dog and if it is a cat (knowing it is a dog makes it certain that it is not a cat).
(notice, knowing one bit of information changes the likelihood of the other being true also).
what is that (n over k) thing in the binomial equation?
n choose k
it tells you how many ways you can choose k objects from a set of n things.
The formula is n!/(n!(n-k)!)
the two numbers on bottom add to the number up top.
These are coefficients in expanded binomials and can also be found in Pascal’s Triangle
What is the “mean of a random variable?”
The expected value.
What you expect to win or get, on average, if you play once.
sum of (probabilities times values)
when can you expect the first success always?
as an example, if there is a 30 percent chance of success?(mean of geo)
1/p
(this is the mean of the geo model)
1/.30. Which is 3.333 so around the 3rd or 4th try.
1/p tells you, on average, when the first success will occur
1/p is the mean of the geometric distribution
what is representative?
It means that the sample statistics will be kind of like the population parameters..
The sample “looks like” the population.
Probability of THIS AND THAT?
Multiply
P(this)*P(that) works when independent only,
when not, then
P(this)*P(that|this)
What type of probability when you are looking for at least one success in twelve attempts?
AT LEAST ONE IS ALWAYS 1 - p(NONE)
Or think of simply not zero
1-all failures
1-qqqqqqqqqqqq
1-q12
1-binopdf(12, p, 0)
What is the “hot hand?”
a misinterpretation of the law of large numbers. Using this law, if you flipped 4 tails in a row, you’d expect the next one to be another tails, because tails is “hot.” A baseball player who gets three hits in a row, you expect another hit? wrong. Streaks happen randomly.
How many ways can you choose 3 books to take with you on a trip out of the 7 books on the shelf?
7 choose 3.
7! / (3! * 4!)
notice that the two factorials on bottom add to the top.
what is n! ?
it is “n factorial”
example: 5! = 5*4*3*2*1= 120.
tells you how many ways you can arrange n objects.
What type of probability when you are looking for more than 5 successes in twelve attempts?
BINO. (notice it is not a “first success” scenario)
6 or more same as not 5 or less
1 - binocdf(12, p, 5)
what does binomial model tell us about?
exactly x successes in K trials.
Like, what is likelihood of exactly 3 heads out of 13 flips?
what is probability?
THE LONG RUN RELATIVE FREQUENCY!!
How do you find mean and sd of discreet random variable ? (like if you have a table of values and probabilities?)
put values in L1, probabilities in L2
then run “1-var stats L1,L2” and you get it!
What type of probability when you are looking for exactly 5 or less successes in twelve attempts?
BINOMIAL
binocdf(12, p, 5)
how do you combine probability models?
(play more than one game)
add or subtract the means,
and then ADD THE VARIANCES