Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Statistics formulas > Midterm > Flashcards

Midterm Flashcards

1
Q

Probability Density Function

Expected Value

A

Expected Value: E = ∑xf(x)

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

Probability Density Function

Variance

A

σ² = E(x²) - (E(x))²

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

Linear Transformation

Linear transformation

A

Y = a + bX

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

Linear Transformation

Expected Value

A

μy = a + bμx

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

Linear Transformation

Variance

A

σ² = b²σ²x

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

Normal Distribution of X

Distribution

A

x ~ N(μ,σ²)

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

Normal Distribution of X (population)

Z = ?

A

Z = (X - μ)/σ ~N(0,1)

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

Sample normal distribution of X (sample)

Distribution

A

X̂ ~ N(μ,σ²/n)

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

Sample normal distribution of X (sample)

Z

A

z = (X - μ)/ (σ/√n) ~ N(0,1)

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

Binomial Probability

Probability of k successes

A

P(Y=k) = (n k)p^k(1-p)^n-k

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

Binomial Probability

E(Y) =

A

E(Y) = np

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

Binomial probability

V(Y) =

A

V(Y) = np(1-p)

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

Binomial Probability

Distribution

A

X~Bin(n,p)

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

Joint pdf

Covariance X,Y

A

σx,y = E(XY) - E(X)*E(Y)

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

Joint pdf

E(XY)

A

E(XY) = ∑xyh(x,y)

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

Joint pdf

correlation x,y

A

ρ = σx,y/σx*σy

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

Linear combination W

W =

A

W = a + bX + cY

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Linear combination W

Expected value

A

E(w) = μw = a + bμx + cμy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Linear combination W

Variance

A

v(x) = σ²w = b²σ²x +2bcσxy + c²σ²y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Test procedure (σ known)

Z test

A

Z = (X - μ)/ (σ/√n)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Test procedure (s known)

T test

A

T = (X - μ)/ (S/√n) ~t(n-1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Test procedure (s known)

CI T test

A

CI = X ∓ tα/2;n-1 * S/√n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Proportion test

A

Z = P^ - p / √p(1-p)/n

24
Q

proportion test

CI

A

ci =p̂+- zα/2 * √p̂(1-p̂)/n

25
Q

Variance test

A

W = (n-1)S²/σ²

26
Q

Variance test

CI

A 
L = (n-1)S²/xα/2;n-1
U = (n-1)S²/1-xα/2;n-1
27
Q

Simple linear regression

Basic assumption

A

E(y|x) = β0 + β1X

28
Q

Simple linear regression

sample equation

A

ŷ = B0 + B1X

29
Q

Simple linear regression

Covariance

A

Sx,y = 1/n-1 ( ∑XiYi - nXYhat) Also = rxy * Sx * Sy

30
Q

Simple linear regression

Variance

A

Sx² = 1/n-1 (∑x²i) - n(x̄)²

31
Q

Simple linear regression

Slope

A

B1 = Sx,y/S²x = (rxySxSy)/ S²x

32
Q

Simple linear regression

Intercept

A

B0 = Yhat - B1x̄

33
Q

Simple linear regression

Residual

A

ei = Yi - Y^i

34
Q

Simple Linear Regression

SSR

A

SSR = B1²(n-1)S²x

35
Q

Simple Linear Regression

correlation

A

rx,y = Sx,y/Sx*Sy

36
Q

Simple linear regression

SST =

A

SST = SSR + SSE = (n-1)Sy^2

37
Q

Simple linear regression

MSE

A

MSE = SSE/n-2 = S²e

38
Q

Simple linear regression

standard error slope

A

SB1 = Se/√(n-1)*S²x

where Se = √MSE

39
Q

Simple linear regression

Regression test for slope

A

T = B1- β1/ SB1 ~ t(n-2)

40
Q

Simple linear regression

Regression slope CI

A

CI = B1 +- tα/2;n-2*SB1

41
Q

Simple linear regression

Coefficient of determination

A

R² = SSR/SST = 1 - SSE/SST

R²adj = 1 - SSE/SST *n-1/n-k-1

42
Q

Uniform probability

Distribution

A

X ~ U(α,β)

43
Q

Uniform probability

E(X)

A

E(X) = a+b/2

44
Q

Uniform probability

V(x)

A

V(X) = (b-a)²/12

45
Q

Uniform probability

Probability P(X<=x)

A

P(X<=x) = x-a/range

46
Q

Confidence interval standard formula

A

CI = sample stat +- critical value α/2 * Standard error

47
Q

MSR =

A

MSR = SSR / df

48
Q

Type I error

A

Wrongfully reject H0

49
Q

Type II error

A

Wrongfully accept H0

50
Q

If the question is about means and you know the POPULATION standard deviation ?

A

Z test

51
Q

If the question is about means and you know the SAMPLE standard deviation ?

A

T test

52
Q

If the questions is about regression, use the test for the slope.

A

T = b1- beta1/ SB1 ~ t(n-2)

53
Q

Proportion test

P^ =

A

P^ = x/n

54
Q

Expectation of sample x

E(x̄) =

A

E(x̄) = μ

55
Q

Variance of sample x

V(x̄) =

A

V(x̄t) = σ²/n

56
Q

Standard deviation of sample x

SD(x̄) =

A

SD(x̄) = σ/√n

Statistics formulas (3 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions