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36 Terms

1
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What is the P(X=x) of a Bernoulli distribution
P(X=1) = p and P(X=0) = 1−p.
2
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What is the E[X] of a Bernoulli Distribution
p
3
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What is the Var(X) of a Bernoulli Distribution

p(1-p)

4
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What is the P(X=k) of a Binomial distribution
P(X=k) = (nk)p^k(1−p)^n−k
5
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What is the expected value (E[X]) of a Binomial distribution
np
6
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What is the variance (Var(X)) of a Binomial distribution
np(1 − p)
7
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What is the P(X=x) of a Geometric distribution
P(X = k) = p(1 − p)^(k−1)
8
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What is the expected value (E[X]) of a Geometric distribution
1/p
9
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What is the variance Var(X) of a Geometric distribution
(1 − p)/p^2.
10
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What is the P(X=x) of a Poisson distribution
P(X=k) = (μ^k/ k!) e^−μ
11
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What is the expected value (E[X]) of a Poisson distribution
μ
12
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What is the variance (Var(X)) of a Poisson distribution
μ
13
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What is the probability density function (PDF) of an Exponential distribution
f(x) = λe^(−λx)
14
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What is the cumulative distribution function (CDF) of an Exponential distribution
F(x) = 1 − e^−λx
15
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What is the expected value (E[X]) of an Exponential distribution
1/λ
16
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What is the variance (Var(X)) of an Exponential distribution
1/λ^2
17
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What is the probability density function (PDF) of a Normal distribution
f(x) = (1/σ√(2π))e^−(x−μ)^2 / (2σ^2)
18
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What is the probability density function (PDF) of a Uniform distribution
f(x) = 1 / (b − a)
19
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What is the cumulative distribution function (CDF) of a Uniform distribution
F(x) = (x − a) / (b − a)
20
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What is the expected value (E[X]) of a Uniform distribution
(a + b)/2
21
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What is the variance (Var(X)) of a Uniform distribution
(b − a)^2/12
22
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Cov(X,Y)

E[(X−E[X])(Y −E[Y])]

23
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Cov(X, Y) (Alternate expression)

E [XY] − E [X] E [Y]

24
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Var(X+Y)=

Var(X)+Var(Y)+2Cov(X,Y)

25
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Correlation coefficient P(X,Y)=

Cov(X,Y)/ sqrt(Var(X)Var(Y))

26
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Var(Y)/a²

P(|Y−E[Y]| ≥ a) ≤

27
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Var(X) =

E[(X-E[X])²]

28
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Sn²=

n/n-1*(Var(X))

29
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(AnB)u(CnD) =

(AuC)n(BuD)

30
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To divide items amongst things

C(n+r-1)_(r-1)

31
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Number of ways you can order n items

N!

32
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Number of ways you can order c1,c2,….,cn objects into groups

n!c1!c2!…cn!

33
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Orders of n objects of which n1 are indistinguishable

n1 objects of which n2 are indistinguishable

.

.

.

nr-1 of which n are indistinguishable

n!/n1!n2!…nr!

34
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How many distinct ordered sets of length r can be formed from n distinct objects

Pn_r = n!/(n-r)!

35
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A’nB’

(AuB)’

36
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(AnB)’

A’uB’