Four temperature gauges are randomly selected from a bin containing seven such gauges. Unknown to the scientist, three of the seven gauges give improper temperature readings. Let X denote the number of defective gauges selected and Y the number of nondefective gauges selected.
a) Find the marginal densities for both X and Y. What type of random variable is Y?
b) Intuitively speaking, are X and Y independent? Jusify your answer mathematically.