0 K/s 42 14 10:24 2 (2020) William Navidi... [ : Jointly Continuous Random Variables We have seen that if X is a continuous random variable, its probabilities are found by integrating its probability density function. We say that the random variables X and Y are jointly continuous if their probabilities are found by integrating a function of two variables, called the joint probability density function of X and Y. To find the probability that X and Y take values in any region, we integrate the joint probability density function over that region. Example 2.54 shows how. Example 2.54 Assume that for a certain type of washer, both the thickness and the hole diameter vary from item to item. Let X denote the thickness in millimeters and let Y denote the hole diameter in millimeters, for a randomly chosen washer. Assume that the joint probability density function of X and Y is given by f(x.y) = "(+y) ifIsx52and4 Sys5 otherwise Find the probability that a randomly chosen washer has a thickness between 1.0 and 1.5 mm, and a hole diameter between 4.5 and 5 mm. Page 130 Solution We need to find P(1 s X