The lifetime (in years) of a light bulb has a continuous distribution with probability density function
For a fixed , find the probability the bulb survives at least time .
Find the probability that the bulb’s lifetime is between one and two years.
[2]
Find the median of the random variable (i.e. with pdf for and otherwise).
Find and when has probability density function given by
[4]
Let be a uniformly distributed random variable with parameters 0 and 1. Let , so that is a random variable taking values in .
For arbitrary , find
Find the probability density function of . What is the distribution of ?
[4]