Chapter 3

Question 1

What to do in joint continuous distribution?

Answer 1

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

Question 2

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

Answer 2

No

Question 3

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

Answer 3

No

Question 4

Cov(x,y) = ?

Answer 4

E(x⋅ y) - E(x) ⋅ E(y)

Question 5

𝜌_x,y = Corr[X, Y] = ?

Answer 5

Cov(x,y)/(SD(x) ⋅ SD(y))

Question 6

Multinomial distribution

Answer 6

n!/x_i! ⋅ P(x_i)

Question 7

E(s) = ?

Answer 7

n ⋅ E(x_i)

Question 8

VAR(s) = ?

Answer 8

n ⋅ VAR(x_i)

Question 9

E(x̄) = ?

Answer 9

E(x_i)

Question 10

VAR(x̄) = ?

Answer 10

VAR(x_i)/n

Question 11

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

Answer 11

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

Question 12

Continuous correction?

Answer 12

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

Question 13

Order statistic min

Answer 13

(S_x(x))^n

Question 14

Order statistic max

Answer 14

(F_x(x))^n

Question 15

Shortcut for continuous uniform

Answer 15

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

Question 16

Shortcut for exponential

Answer 16

E(x_min) = θ/n