Exam 1

Question 1

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

Answer 1

binomial

Question 2

Equation of the binomial coefficient (n k)

Answer 2

n! / k! (n-k)!

Question 3

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

Answer 3

disjoint, partitions

Question 4

Demorgan’s Law

Answer 4

(A ⋃ B)c = Ac ⋂ Bc
(A ⋂ B)c = Ac ⋃ Bc

Question 5

P(Ø) = _____

Answer 5

0

Question 6

P(S) = ______

Answer 6

1

Question 7

if A⊆B, then P(A) ____ P(B)

Answer 7

≤

Question 8

Inclusion-Exclusion Principle

Answer 8

P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)

Question 9

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

Answer 9

0

Question 10

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

Answer 10

P(A) + P(B)
1 - P(Ac)
Ø

Question 11

Events A and B are independent if . . .

Answer 11

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

Question 12

Conditional Probability

Answer 12

P(A | B) = P(A ⋂ B)/ P(B)

Question 13

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

Answer 13

P(A | B) ⋅ P(B) OR
P(B | A) ⋅ P(A)

Question 14

Alternative formula for conditional probability

Answer 14

P(A | B) = [P(B | A) ⋅ P(A)] / P(B)

Question 15

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

Answer 15

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

Question 16

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

Answer 16

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

Question 17

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

Answer 17

does NOT equal

Question 18

Baye’s Theorem

Answer 18

P(A | B) = [P(B | A) ⋅ P(A)] / P(B)

Question 19

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

Answer 19

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

Question 20

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

Answer 20

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

Question 21

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

Answer 21

Function F(X) = P(X ≤ x)

Question 22

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

Answer 22

F(b) - F(a)

Question 23

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

Answer 23

weighted, probabilities

Question 24

E(X) = _________

Answer 24

∑ xn ⋅ P(X = xn)

Question 25

E(X^2) = _________

Answer 25

∑ xn^2 ⋅ P(X = xn)
- square each x value not probability

Question 26

E(c) = _____

Answer 26

c

Question 27

E(X + Y) = _______

Answer 27

E(X) + E(Y)

Question 28

E(X + c) = _______

Answer 28

E(X) + c

Question 29

E(cX) = _______

Answer 29

c ⋅ E(X)

Question 30

Var(X) = __________

Answer 30

E[ (X - E(X))^2 ] OR
E(X^2) - [E(X)]^2

Question 31

The standard deviation is calculated as ___________ and is used to report since its units ___________

Answer 31

SD = √Var(X), are NOT squared

Question 32

Var(c) = ______

Answer 32

0

Question 33

Var(X + c) = _______

Answer 33

Var(X) + 0

Question 34

Var(c ⋅ X) = _______

Answer 34

c^2 ⋅ Var(X)

Question 35

If X and Y are independent,
Var(X + Y) = ________

Answer 35

Var(X) + Var(Y)

Question 36

To calculate F(X) where P(X ≤ xk)

Answer 36

∑ P(X = x) up to the value of xk
Basically sum all prior probabilities

Question 37

For mutually exclusive events A and B,
P(A ⋂ B) = ____

Answer 37

0

Question 38

For independent events A and B,
P(A ⋃ B) = _________

Answer 38

P(A) + P(B) - P(A and B)

Question 39

If A and B are not disjoint then,
P(A ⋃ B) = _________

Answer 39

P(A) + P(B) - P(A ⋂ B)

Question 40

How do you determine if events are mutually exclusive?

Answer 40

P(A ⋂ B) = 0

Question 41

For mutually exclusive events A and B,
P(A ⋃ B) = _________

Answer 41

P(A) + P(B)

Question 42

Mutually exclusive is also known as ____

Answer 42

disjoint