The volume of a cylinder is given by V = πr²h, where r is the radius of the cylinder and h is the height. Assume the radius, in cm, is lognormal with parameters μ r = 1.6 and σ² r = 0.04 , the height,...

The volume of a cylinder is given by V = πr²h, where r is the radius of the cylinder and h is the height. Assume the radius, in cm, is lognormal with parameters μ_r
= 1.6 and σ²_r
= 0.04 , the height, in cm, is log-normal with parameters μ_h
= 1.9 and σ²_h
= 0.05, and that the radius and height are independent. a) Show that V is lognormally distributed, and compute the parameters μ_V
and σ²_V. (Hint: ln V = ln π+2 ln r + ln h.) b) Find P(V < 600).="" c)="" find="" p(500="">< v="">< 800).="" d)="" find="" the="" mean="" of="" v.="" e)="" find="" the="" median="" of="" v.="" f)="" find="" the="" standard="" deviation="" of="" v.="" g)="" find="" the="" 5th="" percentile="" of="" v.="" h)="" find="" the="" 95th="" percentile="" of="">