NAME: .................................................................. NEPTUN-CODE: ....................
Extra Repeated 2nd Test — 2015-12-14 Monday, 8am
60 minutes - Write, please, each problem on a separate sheet. Both mathematical and Excel formulas are accepted.
1.
The distribution function of the random variable X is x
1 , 5
(0 ≤ x ≤ 1) . Calculate the variance of X .
2.
Five people, independently of each other, arrive at a casino between midnight and 1 a.m. according to uniform distribution. Let
X be the time instant when the second person arrives. (Time is measured in hours, which means, for example: if the second arrives at 0:30, then X = 0 .
5 .) Calculate the expected value of X .
3.
X follows exponential distribution with an expected value 0.5. If X = x , then Y follows exponential distribution with parameter x . Determine the (unconditional) density function of Y .
4. a) Write a formula in Excel to simulate the random variable X defined in problem one.
b) How would you approximate - with a simulation in Excel - the expected value of X defined in problem two?
You may give your answer to question b) in a tabular form as if you worked in Excel, or with sentences in a brief clear form.
NAME: .................................................................. NEPTUN-CODE: ....................
Extra Repeated 2nd Test — 2015-12-14 Monday, 8am
60 minutes - Write, please, each problem on a separate sheet. Both mathematical and Excel formulas are accepted.
1.
The distribution function of the random variable X is x 1 , 5 (0 ≤ x ≤ 1) . Calculate the variance of X .
2.
Five people, independently of each other, arrive at a casino between midnight and 1 a.m. according to uniform distribution. Let
X be the time instant when the second person arrives. (Time is measured in hours, which means, for example: if the second arrives at 0:30, then X = 0 .
5 .) Calculate the expected value of X .
3.
X follows exponential distribution with an expected value 0.5. If X = x , then Y follows exponential distribution with parameter x . Determine the (unconditional) density function of Y .
4. a) Write a formula in Excel to simulate the random variable X defined in problem one.
b) How would you approximate - with a simulation in Excel - the expected value of X defined in problem two?
You may give your answer to question b) in a tabular form as if you worked in Excel, or with sentences in a brief clear form.
NAME: .................................................................. NEPTUN-CODE: ....................
Extra Repeated 2nd Test — 2015-12-14 Monday, 8am
60 minutes - Write, please, each problem on a separate sheet. Both mathematical and Excel formulas are accepted.
1.
The distribution function of the random variable X is x 1 , 5 (0 ≤ x ≤ 1) . Calculate the variance of X .
2.
Five people, independently of each other, arrive at a casino between midnight and 1 a.m. according to uniform distribution. Let
X be the time instant when the second person arrives. (Time is measured in hours, which means, for example: if the second arrives at 0:30, then X = 0 .
5 .) Calculate the expected value of X .
3.
X follows exponential distribution with an expected value 0.5. If X = x , then Y follows exponential distribution with parameter x . Determine the (unconditional) density function of Y .
4. a) Write a formula in Excel to simulate the random variable X defined in problem one.
b) How would you approximate - with a simulation in Excel - the expected value of X defined in problem two?
You may give your answer to question b) in a tabular form as if you worked in Excel, or with sentences in a brief clear form.