Question

1. Which of the following is a probability mass function for some probability distribution p with domain {1,2,3,4}?

		P(1)=0.1,P(2)=0.2,P(3)=0.3,P(4)=0.4
		P(1)=0.1,P(2)=0.1,P(3)=0.3,P(4)=0.4
		P(1)=0.2,P(2)=0.4,P(3)=0.3,P(4)=0.4
		P(1)=-0.5,P(2)=0.8,P(3)=0.5,P(4)=0.2

2. Let X be the random variable where X is the number of heads after flipping a fair coin 50 times. What is the mean of X?

3. Suppose that one flips a fair coin 6 times. What is the probability of getting at most 2 heads?

4.

Which of the following is a discrete probability distribution and not a continuous probability distribution?

		Cauchy distribution
		Normal distribution
		Chi-square distribution
		Binomial distribution

5. Suppose that one flips a fair coin 6 times. What is the probability of getting an even number of heads?

6. What is the mean of the following distribution (the unit m stands for meters):

P(1m)=0.1,P(2m)=0.2,P(3m)=0.3,P(4m)=0.4?

		3m^2
		3m
		3m^3
		3

7. Find the variance of the following probability distribution.

P(0)=1/16,P(1)=4/16,P(2)=6/16,P(3)=4/16,P(4)=1/16.

8. Suppose that one flips a fair coin 10 times. What is the probability that the coin will land on heads 6 times and tails 4 times.

9.Find the mean of the following probability distribution. Do not use a calculator or any other computational aid.

P(0)=0.1,P(1)=0.3,P(2)=0.4,P(3)=0.2

10. Consider the random variable X where X is the number of times one gets heads when flipping an unfair coin 100 times where there is a 2/5 chance of getting heads and a 3/5 chance of getting tails. What is the variance of X?

Answer 1