4

Question 1

Random variable X?

Answer 1

A function from the state space to the real numbers.

Question 2

Discrete variable?

Answer 2

A random variable that produces a countable set.

Question 3

Probability mass function (PMF)?

Answer 3

For each a in countable set -> p(a) + P{X = a}

Question 4

Cumulative distribution function?

Answer 4

Probability of getting less or equal to a value: F(a) = P{X <= a} = sum(x<=a)(p(x))

Question 5

Expectation?

Answer 5

The average value you would expect from a probability distribution.

Question 6

Expectation of X as E[X] = ?

Answer 6

Sum(p(x) > 0)(k P(x = k))

Question 7

Expectation of X if the state space is countable, E[X] = ?

Answer 7

Sum(s (- S)(P{s} X(s))

Question 8

E[g(X)] = ?

Answer 8

Sum(p(x) > 0)(g(x) p(x))

Question 9

Sum(X)(p(X)) = ?

Answer 9

1

Question 10

E(X^2) = ?

Answer 10

Sum(X)(X^2 p(X))

Question 11

E[aX + b] = ?

Answer 11

aE[X] + b

Question 12

E[X + Y] = ?

Answer 12

E[X] + E[Y]

Question 13

E[aX] = ?

Answer 13

aE[x]

Question 14

Register exams

Question 15

Variance (sigma^2): Var(X) = ? (2•)

Answer 15

•E[((X - mu)^2)] = E[((mu - X)^2)], alt •E[X^2] - (E[X])^2

Question 16

p(a) = ?

Answer 16

P({x = a})

Question 17

Var[aX] = ?

Answer 17

a^2 Var[X]

Question 18

Standard Deviation (sigma): SD[X] = ?

Answer 18

(Var[X])^(1/2)

Question 19

SD[aX] = ?

Answer 19

aSD[X]

Question 20

Formula of SD for a uniform finite distribution?

Answer 20

(((sum(mu - x))^2 / n))^(1/2)