XMA401 Probability distributions and Statistical Methods

A random variable has the following probability distribution X = xi 1 2 3 4 P(X=xi) 0.1 0.2 0.3 0.4 The mean is -----

Var (ax +b) is

• a. Var (X)

• a^2 Var (X)

• a^2 Var (X) + b

• a Var (X) + b

An event in the probability that will never be happened is called as -----

• a. Unsure event

• b. Sure event

• c. Possible event

• d. Impossible event

E (XY) = E (X).E (Y) if X and Y are independent. Say True or False.

• True

• False

A card is drawn from a pack of 52 cards. What is the probability of getting a king of a black suit?

• 1/26

• 1/52

• 2/26

• 7/52

Out of the following values, which one is not possible in probability?

• a. p(x) = 1

• b. ∑ x p(x) = 3

• c. p(x) = 0.5

• d. p(x) = - 0.5

The probability of getting two tails when two coins are tossed is ----

• a. 1/6

• b. 1/2

• c. 1/3

• d. 1/4

If the mean of a distribution is 25 and the fourth moment about the mean is 500, what is the kurtosis of the distribution?

• 2.5

• 3.0

• 3.5

• 4.0

What is the variance of 3X + 2Y if Var(X) = 4 and Var(Y) = 9?

• 4

• 9

• 16

• 25

If the probability of drawing a red ball from a bag is 1/4 and the probability of drawing a blue ball is 1/3, what is the probability of drawing either a red or a blue ball?

• 1/2

• 5/12

• 7/12

• 2/3