Probability

Question 1

Define unimodal and bimodal

Answer 1

one peak vs 2 peaks in histogram

Question 2

define postive skew

Answer 2

tail towards larger values. This causes mean to be further towards the right than the median.

Question 3

N vs n?

Answer 3

N= large population n= sample population

Question 4

proof that sample mean on a balance beam is where the clockwise and anti clockwise moment is =

Answer 4

probability lecture 1. 20 mins

Question 5

what is variance?

Answer 5

how spread out the data is

Question 6

Define: A,B
A u B
A n B
A'
A/B'

Answer 6

first A and B
A or B
A and B
Not A
A but not B

Question 7

If A n B is not 0 how does A effect B

Answer 7

A doesnt effect B, both are mutually exclusive.

Question 8

What are the three axioms of probability theory?

Answer 8

Axiom 1: For any event A ⊂ S, P(A) ≥ 0.
Axiom 2: P(S) = 1
Axiom 3: If A1, A2, A3, … is an infinite collection of mutually-exclusive events, then P(A1 ∪ A2 ∪ A3 ∪ …) = 1

Question 9

what are the properties of probability?

Answer 9

1. For any event A, P(A) = 1 − P(A
   0
   ).
2. Monotonicity: if A ⊆ B then P(A) ≤ P(B).
3. Probability of the empty set: P(Ø) = 0.
4. Numerical bound: 0 ≤ P(A) ≤ 1.
5. P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Question 10

in conditional probability when are two events independent?

Answer 10

Two events are independent if P(A|B) = P(A)
Proposition: Two events A and B are independent if and only if
P(A ∩ B) = P(A)P(B).

Question 11

what is a bernoulli random variable?

Answer 11

variable which only takes values 1 or 0

.

Question 12

what is the cumulative distribution function?

Answer 12

total probability until value of x reached. lec 2 23mins