Chapter 3 Flashcards

1
Q

What to do in joint continuous distribution?

A

Do a 3D graph to see which square do you have to calculate.

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2
Q

If Cov(x,y) = 0 are x and y necessarily independent?

A

No

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3
Q

If E(x ⋅ y) = E(x) ⋅ E(y) are x and y necessarily independent?

A

No

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4
Q

Cov(x,y) = ?

A

E(x⋅ y) - E(x) ⋅ E(y)

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5
Q

𝜌_x,y = Corr[X, Y] = ?

A

Cov(x,y)/(SD(x) ⋅ SD(y))

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6
Q

Multinomial distribution

A

n!/x_i! ⋅ P(x_i)

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7
Q

E(s) = ?

A

n ⋅ E(x_i)

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8
Q

VAR(s) = ?

A

n ⋅ VAR(x_i)

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9
Q

E(x̄) = ?

A

E(x_i)

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10
Q

VAR(x̄) = ?

A

VAR(x_i)/n

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11
Q

VAR(x) = ? using the law of total variance

A

E(VAR(X|Y)) + VAR(E(X|Y))

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12
Q

Continuous correction?

A

If x > 3 —> x > 3.5
If x< 3 —> x < 2.5

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13
Q

Order statistic min

A

(S_x(x))^n

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14
Q

Order statistic max

A

(F_x(x))^n

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15
Q

Shortcut for continuous uniform

A

E(x_min) = a + (b-a)/n+1
E(x_max) = b - (b-a)/n+1

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16
Q

Shortcut for exponential

A

E(x_min) = θ/n