Other stats (combination of linear variables)

Question 1

How do you find an unbiased estimate of the variance of a population from sample?

Answer 1

s^2 = n/(n-1) x (Var(x))

Question 2

How do you find an unbiased estimate of the population mean from the sample?

Answer 2

Unbiased estimate of the mean = (Sum of x)/n

Question 3

Var(X + Y) = ?

Answer 3

Var(X + Y) = Var(X) + Var(Y)

Question 4

Var(aX+c) = ?

Answer 4

Var(aX+c) = a^2Var(X)

Question 5

E(aX + bY + c) = ?

Answer 5

E(aX + bY + c) = aE(X) + bE(Y) + c

Question 6

Var(aX + bY + c) = ?

Answer 6

Var(aX + bY + c) = a^2Var(X) + b^2Var(Y)

Question 7

Var(X_1 + X_2) = ?

Answer 7

Var(X_1 + X_2) = Var(X_1) + Var(X_2)

Question 8

Var(2X) = ?

Answer 8

Var(2X) = 4Var(X)

Question 9

Var(x̄) = ?

x̄ means sample _ and X means population

Answer 9

Var(x̄) = Var(X)/n

Question 10

E(x̄) = ?

x̄ means sample _ and X means population

Answer 10

E(x̄) = E(X)

Question 11

What happens if you sum random variables which follow a normal distribution?

Answer 11

The sum of variables will also follow a normal distribution

Question 12

Define the Central Limit Theorem

Answer 12

For any distribution,
if E(X) = a, Var(X) = b^2, and n>25, then the approximate distributions are given by:

x̄ ~ N(a, b^2/n)