Chapter 7: DRV and Expectation.

Question 1

What do the sum of all probabilities add to?

Answer 1

1.

Question 2

What is E(X)?

Answer 2

The Expectation of X.

Question 3

What is E(X^2)?

Answer 3

The Expectation of X squared.

Question 4

What is the Formula for the E(X)?

Answer 4

∑((x) x P(X=x)) - Sum of the value of x multiplied by the probability of x.

Question 5

What is the Formula for the E(X^2)?

Answer 5

∑((x^2) x P(X=x)) - Sum of the value of x^2 multiplied by the probability of x.

Question 6

What is the Formula for the Var(X)?

Answer 6

Var(X) = E(X^2) - (E(X))^2

Question 7

What does E(aX+b) equal?

Answer 7

aE(X) + b

Question 8

What does Var(aX+b) equal?

Answer 8

a^2Var(X)

Question 9

What is the mean of E(X)?

Answer 9

1/2(n+1)

Question 10

What is the mean of Var(X)?

Answer 10

1/12(n-1)(n+1)

Question 11

How do you find Standard Deviation from Variance?

Answer 11

S.D = square root of Variance.

Question 12

For 2 discrete independent random variables, the expected value of the sum - E(X+Y) equals?

Answer 12

E(X+Y) = E(X) + E(Y).

Question 13

For 2 discrete independent random variables, the variance of the sum - Var(X+Y) equals?

Answer 13

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

Question 14

What is an example of a probability density function (p.d.f)?

Answer 14

P(X = x).

Question 15

What is the modal value?

Answer 15

The most frequent result.

Question 16

What is the name of the distribution given to the discrete random variable T?

Answer 16

Discrete Uniform Distribution.

Question 17

How do you find the median?

Answer 17

When the probabilities either side are equal to 0.5.