Final Exam [Short Answer/TF]

Question 1

A committee of two needs to be formed from a group of 6 people. How many possible selections are there?

Answer 1

15

Question 2

Let A and B be two events, both of which have positive probabilities. If P(A │ B) = P(A), what is true about events A and B?

Answer 2

They are independent

Question 3

Let X~Geom(p) with an E(X) = 4. What is the value of p?

Answer 3

1/5

Question 4

Let X~N(μ = 2, σ = 2). What is the approximate value of P( 0 < X < 4)?

Answer 4

0.68

Question 5

What discrete distribution also has the forgetfulness/ memoryless property?

Answer 5

Geometric

Question 6

If Y~Unif(-2,2), what is E(Y)?

Answer 6

0

Question 7

If X~Exp(λ), then E(X) is _____ 0.

Answer 7

E(X) > 0

Question 8

Given that X~N(μ, σ²), SD(X - 1) = __________

Answer 8

SD(X - 1) = SD (X)

Question 9

If X~Bin(1, p), then it is equivalent to which other distribution?

Answer 9

Bernoulli with parameter p

Question 10

[T/F] If E(X) > 0, then X can only take on positive value?

Answer 10

False

Question 11

[T/F] If X~Pois(1.5), then P(X = 1.5) = 0.

Answer 11

True

Question 12

[T/F] If Z~N(0,1), then P(Z = 0) = 0.5.

Answer 12

False

Question 13

[T/F] If X~Exp(λ), then E(X) > SD(X).

Answer 13

False

Question 14

[T/F] For any random variable X, E(X^2) cannot be negative.

Answer 14

True

Question 15

A negative binomial distribution with only one success is equivalent to what other distribution?

Answer 15

Geometric

Question 16

[T/F] The support of the exponential distribution is finite.

Answer 16

False

Question 17

6 people run a race, how many possible combinations of winners (1st, 2nd, 3rd) are there?

Answer 17

120

Question 18

Based on the rules of expected value, E(X -1) = _____

Answer 18

E(X -1) = E(X) -1

Question 19

[T/F] If the correlation between two random variables X and Y is zero, then they are independent.

Answer 19

False

Question 20

[T/F] Covariance is always between -1 and 1.

Answer 20

False

Question 21

[T/F] If two events A and B are independent, then P(A ∩ B) = 0.

Answer 21

False

Question 22

[T/F] Discrete random variables always have a finite support.

Answer 22

False

Question 23

[T/F] For any events A and B, P(A ∪ B) = P(A) + P(B).

Answer 23

False

Question 24

[T/F] For any event A and its complement Ac,
P(A ∩ Ac) = 1

Answer 24

False

Question 25

[T/F] If two random variables are independent then they are also uncorrelated.

Answer 25

True

Question 26

[T/F] If two random variables have the same CDF, the random variables follow the same distribution.

Answer 26

True

Question 27

[T/F] If a random variable has a finite variance, it must also have a finite mean.

Answer 27

True

Question 28

[T/F] For any events A and B, P(A ∪ B) is always less than P(A).

Answer 28

False