7. For the following problems, write down how you would code the probabilities requested into R. You should use the specialized distribution functions mentioned in the lecture notes from Sections 5.2-5.5. There is one problem for each distribution (Binomial, Poisson, Geometric, and Hypergeometric). You do not need to provide the final answer. (a) Suppose X Bin(18, 0.42). Find P(X < 11). (b) Suppose a box shipped to Jennifer's Restaurant contains 300 cupcakes. For some reason, there were 25 smashed cupcakes in the box. A manager randomly chooses 12 cupcakes for inspection. The manager wants to know the probably that, among the 12, that 3 or less are smashed. (c) Suppose X Pois(t = 13). Find P(X 9). (d) Suppose X Geom(p = 0.43). Define X to be the number of trials until the first success occurs. We want to find P(X = 4). Note: Be sure to check out how R defines a geometric random variable.