solve these problems

Consider the density function JKVI, 02, Y = 1); c) (C) PIX > Y);(d) F(X + Y = 4). A coin is flipped until 3 heads in succession occur. List only those elements of the sample space that require 6 or less tosses. Is this a discrete sample space? Explain.A continuous random variable X that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 + x)/27. Find (a) P(X 0. y>0. elsewhere, find P(0 2).The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function 20.000 f(x) = (x+ 100)4+ elsewhere. Find the probability that a bottle of this medicine will have a shell life of (a) at least 200 days; (b) anywhere from 80 to 120 days.The amount of kerosene, in thousands of liters, in a tank at the beginning of any day is a random amount Y from which a random amount X is sold during that day. Suppose that the tank is not resupplied during the day so that x y, and assume that the joint density function of these variables is f(x, y) = (2, 0