solve the following question

For the density function of Exercise 3.18, find F(x), and use it to evaluate P(3 s X 3); (c) P(1.4 2).Referring to Exercise 3.38, find (a) the marginal distribution of X; (b) the marginal distribution of Y. Reference: Exercise 3.38: If the joint probability distribution of X and Y is given by RX, y) = 30 Ity, for x = 0, 1, 2, 3; y = 0, 1, 2, find a) P(X $2, Y= 1); b) P(X >2, Y= 1); c) (c) P(X >Y):(d) P(X + Y = 4).A cereal manufacturer is aware that the weight of the product in the box varies slightly from box to box. In fact, considerable historical data have allowed the determination of the density function that describes the probability structure for the weight (inounces). Letting X be the random variable weight, in ounces, the density function can be described as (a) Verify that this is a valid density function. (b) Determine the probability that the weight is smaller than 24 ounces. (c) The company desires that the weight exceeding 26 ounces be an extremely rare occurrence. What is the probability that this rare occurrence does actually occur? A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If x is the number of defective sets purchased by the hotel, find the probability distribution of X. Express the results graphically as a probability histogram