Solve the question

Construct a graph of the cumulative distribution function of Exercise 3. 15. Reference: Exercise 3. 15: Find the cumulative distribution function of the random variable X representing the number of defectives in Exercise 3.11. Then using F(x), find (a) P(X = 1); (b) P(0 2).The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X. Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X: (a) f(x) = c(x2 + 4), for x = 0, 1, 2, 3; (b) f(x) = c() (->), for x = 0, 1, 2.The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by 1 2 3 I(x) 0.41 0.37 0.16 0.05 0.01 Construct the cumulative distribution function of X. Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density f (z, y) = - 01/2)