Given the following function: 0

Given the following function: o elsewhere Find the corresponding distribution function and verify that this is a legitimate proba bility density Determine the probability that a random variable having this probability distri- bution will take on a value greater than 1.8 betwen 0.4 and 1.6 The length of satisfactory illumination in years provided by a certain model of lightbulb is a random variable having probability density Find the probabilities that one of these lightbulbs will provide satisfactory illumination for at most 2.5 years between 4 and 6 years at least 6.75 years For the following probability density, find the mean and variance: elsewhere