Exam 1 Flashcards

1
Q

The ______ coefficient is used to choose k out of n objects

A

binomial

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Equation of the binomial coefficient (n k)

A

n! / k! (n-k)!

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

If S is the sample space for any event A⊆S . . .
A ⋂ Ac = Ø, they are _________
A ⋃ Ac = S, they are _________

A

disjoint, partitions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Demorgan’s Law

A

(A ⋃ B)c = Ac ⋂ Bc
(A ⋂ B)c = Ac ⋃ Bc

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

P(Ø) = _____

A

0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

P(S) = ______

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

if A⊆B, then P(A) ____ P(B)

A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Inclusion-Exclusion Principle

A

P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

If A and B are disjoint events then,
P(A ⋂ B) = _______

A

0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

If A and B are disjoint events then,
P(A ⋃ B) = _____
P(A) = _______
P(A ⋂ B) = ____

A

P(A) + P(B)
1 - P(Ac)
Ø

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Events A and B are independent if . . .

A

P(A ⋂ B) = P(A) ⋅ P(B)
P(A | B) = P(A)
P(B | A) = P(B)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Conditional Probability

A

P(A | B) = P(A ⋂ B)/ P(B)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

When working conditionally,
P(A ⋂ B) = ________

A

P(A | B) ⋅ P(B) OR
P(B | A) ⋅ P(A)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Alternative formula for conditional probability

A

P(A | B) = [P(B | A) ⋅ P(A)] / P(B)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

The Law of Total Probability for A1 …. An as partitions of S

A

P(B) = [P(B | A1) ⋅ P(A1)] + [P(B | A2) ⋅ P(A2)]…. up to An

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the practical formula for Baye’s Theorem given that A and Ac are partitions of S?

A

P(A | B) =
P(B | A) ⋅ P(A) / P(B | A) ⋅ P(A) + P(B | Ac) ⋅ P(Ac)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Prosecutor’s Fallacy states that
P(A | B) ______ P(B | A)

A

does NOT equal

18
Q

Baye’s Theorem

A

P(A | B) = [P(B | A) ⋅ P(A)] / P(B)

19
Q

Disjoint events (P(A ⋂ B) = 0) can only be independent if . . .

A

P(A) = 0 OR P(B) = 0

20
Q

What is the probability mass function (PMF) of a d.r.v?
d.r.v = X

A

P(X = x) for all x values in the support of random variable X

21
Q

What is the cumulative distribution function (CDF) of a d.r.v?
d.r.v = X

A

Function F(X) = P(X ≤ x)

22
Q

When describing the CDF of
P(a ≤ X ≤ b) = ________

A

F(b) - F(a)

23
Q

The expected value of a d.r.v is a ________ average of all the possible values X can take on weighted by their ________.

A

weighted, probabilities

24
Q

E(X) = _________

A

∑ xn ⋅ P(X = xn)

25
E(X^2) = _________
∑ xn^2 ⋅ P(X = xn) - square each x value not probability
26
E(c) = _____
c
27
E(X + Y) = _______
E(X) + E(Y)
28
E(X + c) = _______
E(X) + c
29
E(cX) = _______
c ⋅ E(X)
30
Var(X) = __________
E[ (X - E(X))^2 ] OR E(X^2) - [E(X)]^2
31
The standard deviation is calculated as ___________ and is used to report since its units ___________
SD = √Var(X), are NOT squared
32
Var(c) = ______
0
33
Var(X + c) = _______
Var(X) + 0
34
Var(c ⋅ X) = _______
c^2 ⋅ Var(X)
35
If X and Y are independent, Var(X + Y) = ________
Var(X) + Var(Y)
36
To calculate F(X) where P(X ≤ xk)
∑ P(X = x) up to the value of xk Basically sum all prior probabilities
37
For mutually exclusive events A and B, P(A ⋂ B) = ____
0
38
For independent events A and B, P(A ⋃ B) = _________
P(A) + P(B) - P(A and B)
39
If A and B are not disjoint then, P(A ⋃ B) = _________
P(A) + P(B) - P(A ⋂ B)
40
How do you determine if events are mutually exclusive?
P(A ⋂ B) = 0
41
For mutually exclusive events A and B, P(A ⋃ B) = _________
P(A) + P(B)
42
Mutually exclusive is also known as ____
disjoint