Consider the following pdf for the random variable X:

, for 

Which of the following distributions does X follow?

for  and 0 elsewhere.

Calculate .

Consider a continuous random variable X with the following CDF:

for 

What is P(2 < X < 8)?

On the average, a certain computer part lasts ten years. The length of time the computer part lasts is exponentially distributed. Knowing that one of this parts is 5 years old and still working in perfect conditions, what is the probability that lasts by at least more 4 years?

A basketball player has a sucess rate of 75% at each throw he tries to score. What is the probability that he needs to wait until is fourth throw to finally score?

The average number of accidental drownings per year in a country is 2 per 100000 population. The probability that in a city with a population of 200000 there wil be at most 2 accidental drownings per year is,

An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. The mean and variance of the number of wells that must be drilled until the oil company is able to find three wells striking oil are, respectively,

The cumulative distribution function (CDF) of a continuous random variable can have jumps or discontinuities.