2. A hazelnut factory divides hazelnuts into two groups based on their quality X random variable raio of 1st quality hazelnuts, Y Let the random variable show the ratio of 2nd Quality hazelnuts. The common distribution is expressed as follows: ()= 24.0 sS 1.OSS1, +s1 a Calculate the probability P (x+ ys0.5) by checking the validity of the given distribution (10P) b. Draw the shape of the joint density function and show the region under a. (10P) C. Obtain the marginal distribution of X (10P) f (x, y) = 24xy, 0