The density function of the continuous random variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is given. Find the average number of hours per year that families run their vacuum cleaners. f(x) = √√42 3 7 0, - 7 -x, 6' 0

Don't Hand writing in solution.

A random variable X has density 3x2 for 0 < x < 1. Find its variance.(use a decimal number, rounded to the nearest 1,000th. For example, 0.123)

The hypotenuse, Y, of the isosceles right triangle shown 0 is a random variable having a uniform pdf over the interval [5, 10]. Calculate the expected value of the triangle's area. Do not leave the answer as a function of a. (round to 3 decimal places)