Question: Please show work and provide excel formulas for plots so that I can understand how to do the assignment. The density function of a 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 described by the following probability density function:
x for 0 < x < 1
2-x foe 1 < x < 2
0 elsewhere
a. Plot the PDF and CDF between the values of 0 < x < 2
b. What is the average (mean) number of hours per year that families run their vacuum cleaners
c. Find the 60th percentile number of hours per year that families run their vacuum cleaners
d. Find the probability that families run their vacuum cleaners between 50 and 120 hours per year