Module 1 Flashcards
(20 cards)
What happens if A1 and A2 are disjoint sets?
The probability of both occuring Pr(A1 U A2) = Pr(A1) + Pr(A2)
- Literally just add the probability of getting A1 and A2
What does disjoint mean?
That they can’t occur at the same time
What is the probability of sample space?
1
Can the probability of an event be 0?
No
What is the difference between Union and Intersect?
Union is the probability of both events (one or the other) happening
- Everything in both sets
Intersect is the probability of the shared events of both sets happening
- Only what they have in common
If two sets are intersect, what is the probability?
The probability of the intersect of two sets cannot be larger than the probability of A or B
$$Pr(A \cap B) <= min(Pr(A), Pr(B))$$
What is true about the probability of the union of A and B (Two Sets)?
The probability that A and B occur (union) is less than or equal to the sum of Pr(A) + Pr(B)
- $$Pr(A\cup B) <= Pr(A) + Pr(B))$$
If a set is apart of the sample space, then what is true about the probability of the sample space?
Adding all the probabilities together, it equals 1
What is conditional probability?
The probability of event A occuring given B
Pr(A|B)
Which has already occured and which one are we trying to figure out the probability for?
B has already occured
We are trying to find A
How to find Pr(A|B)
$$\Pr(A \mid B) = \frac{\Pr(A \cap B)}{\Pr(B)}$$
The intersect of A and B divided by the probability of B
What are random variables?
Assigning a set of outcomes to a numerical value, we do this to make things simpler
Two events are considered independent if:
$$Pr(A \cap B) = Pr(A)Pr(B)$ or $\Pr(A \mid B) = Pr(A)$$
What is a Discrete Random Variable?
A countable value like the number of heads from 3 coin tosses
What is a Continous Random Variable?
An uncountable value like height or time to finish a race
- Stuff like height isn’t 100% accurate as other factors could affect it
What does CDF stand for and mean?
Cumulative Distribution Function
The probability of all X value in a rnage
Find Pr of X less than or equal to x
ex. Income, find all people who gets paid 100k or less
What does PDF stand for and mean?
Probability Density Function
Probability over an interval
Probability of x falls under a range
Usually for Continous R.V.
Ex. Find the range of people who fall under the range 95k - 105k
What does PMF stand for and mean?
Probability Mass Function: The probability X takes an exact value
Probabiliyt of all X must equal 1
Only uses Discrete Random Variables
What does Expectation mean?
The weighted Average of possible values
