Download 2015-05-06___Sample Test 2015-02

1. The life-time of a certain type of electric bulbs has an exponential
distribution with an average life time of 100 hours.
(a) What is the probability that a bulb of this type will work at least 150
hours?
(b) What is the probability that a bulb of this type having been used
successfully for 150 hours will work at least 100 more hours in addition
to the
150 hours?
2. Assume that a measurement result X has a normal distribution with
expected value 120 and standard deviation 20.
(a) What is the probability that X is larger than 125?
(b) If we know that the measurement result X is larger than 125, then
what is the probability that X is larger than 135?
3. The density function of X is f(x) = 5 x^4 (0 < x < 1).
Let Y = X^2.
(a) Calculate the expected value of X.
(b) Calculate the expected value of Y.
4. The density function of X is f(x) = 5x^4 (0 < x < 1). Let Y = X^2.
(a) Calculate the standard deviation of X.
(b) Calculate the standard deviation of Y.
5. a) Assume that X follows uniform distribution on the interval [10; 20].
What is the probability that X is between 14 and 15?
b) Make 50 independent experiments for X. What is the probability that
average of the 50 experimental results is between 14 and 15?
(You may give your answer in terms of the mathematical function Φ or
of the NORMDIST Excel function.)