Stat 225 - Quiz 2 A+++

Stat 225 - Quiz 2 
1. What is the probability that during the following 10 days Tom has 3 days in a row in which he gets a Coke? (3 points)
2. Now Tom randomly picks three bottles from the fridge for the first three days. What is the probability that he gets two Fantas and one Root Beer? (3 points)
3. Suppose, for this question only, we label each bottle from 1 to 10. When Tom randomly picks up 4 bottles, how many different ordered arrangements are there for these 4 bottles? (3 points)
X is a discrete random variable with the following Probability Mass Function.
X
-2
-1
0
1
2
3
P(X=a)
0.2
0.1
0.3
0.2
0.15
0.05
4. Compute P[X>-1.3] (2 points)
5. Compute E[X] (3 points)
6. Compute E[ ]. That is, calculate the expected value of | |. (3 points)
7. Let Y=-2X. Compute Var[Y] (3 points)
Stat 225 - Quiz 2 Name________________________________________
Group Members' Names_______________________________________________________
09/17/2012
You have 30 minutes to complete the problems below. Show sufficient work to receive full credit. If a decimal answer is not exact, please round to 2 non-zero decimal places.
Tom has 14 bottles of sodas in the fridge, and he will get exactly one bottle of soda per day in the next 14 days. He has 4 Cokes, 3 Fantas, 4 Root Beers, and 3 Sprites. Assume for each kind of soda, the bottles are the same.
1. What is the probability that during the next 14 days Tom has 3 days in a row in which he gets a Fanta? (3 points)
2. Now Tom randomly picks three bottles from the fridge for the first three days. What is the probability that he gets two Root Beers and one Sprite? (3 points)
3. Suppose, for this question only, we label each bottle from 1 to 14. When Tom randomly picks up 4 bottles, how many different ordered arrangements are there for these 4 bottles? (3 points)
X is a discrete random variable with the following Probability Mass Function.
X
-3
-2
-1
0
1
2
P(X=a)
0.15
0.1
0.2
0.25
0.2
0.1
4. Compute P[X>-1.3] (2 points)
5. Compute E[X] (3 points)
6. Compute E[ ]. That is, calculate the expected value of | |. (3 points)
7. Let Y=2X. Compute Var[ ] (3 points)
Stat 225 - Quiz 2 Name________________________________________
Group Members' Names_______________________________________________________
09/17/2012
You have 30 minutes to complete the problems below. Show sufficient work to receive full credit. If a decimal answer is not exact, please round to 2 non-zero decimal places.
Tom has 12 bottles of sodas in the fridge, and he will get exactly one bottle of soda per day in the next 12 days. He has 5 Sprites, 2 Cokes, 3 Root Beers , and 2 Fantas. Assume for each kind of soda, the bottles are the same.
1. What is the probability that during the next 12 days Tom has 3 days in a row in which he gets a Root Beer? (3 points)
2. Now Tom randomly picks three bottles from the fridge for the first three days. What is the probability that he gets two Sprites and one Root Beer? (3 points)
3. Suppose, for this question only, we label each bottle from 1 to 12. When Tom randomly picks up 4 bottles, how many different ordered arrangements are there for these 4 bottles? (3 points)
X is a discrete random variable with the following Probability Mass Function.
X
-2
-1
0
1
2
3
P(X=a)
0.1
0.15
0.25
0.2
0.15
0.15
4. Compute P[X>2.3] (2 points)
5. Compute E[X] (3 points)
6. Compute E[ ]. That is, calculate the expected value of | |. (3 points)
7. Let Y=3X. Compute Var[ ] (3 points)
Stat 225 - Quiz 2 Name________________________________________
Group Members' Names_______________________________________________________
09/17/2012
You have 30 minutes to complete the problems below. Show sufficient work to receive full credit. If a decimal answer is not exact, please round to 2 non-zero decimal places.
Tom has 13 bottles of sodas in the fridge, and he will get exactly one bottle of soda per day in the next 13 days. He has 4 Fantas, 2 Sprites, 4 Root Beers, and 3 Cokes. Assume for each kind of soda, the bottles are the same.
1. What is the probability that during the next 13 days Tom has 3 days in a row in which he gets a Coke? (3 points)
2. Now Tom randomly picks three bottles from the fridge for the first three days. What is the probability that he gets two Fantas and one Coke? (3 points)
3. Suppose, for this question only, we label each bottle from 1 to 13. When Tom randomly picks up 5 bottles, how many different ordered arrangements are there for these 5 bottles? (3 points)
X is a discrete random variable with the following Probability Mass Function.
X
-3
-2
-1
0
1
2
P(X=a)
0.05
0.15
0.25
0.2
0.25
0.1
4. Compute P[X<0.3] (2 points)
5. Compute E[X] (3 points)
6. Compute E[ ]. That is, calculate the expected value of | |. (3 points)
7. Let Y=-4X. Compute Var[ ] (3 points)