3. (7 points) For the following problems, write down how you would code the probabilities requested into R. You should u

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3 7 Points For The Following Problems Write Down How You Would Code The Probabilities Requested Into R You Should U 1 (174.91 KiB) Viewed 14 times

3. (7 points) 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 (20, 0.35). Find P(X>6). (b) Suppose X~ Pois(At = 8). Find P(X < 10). (c) Suppose X Geom (p = 0.75). Define X to be the number of trials until the first success occurs. We want to find P(X ≤ 6). Note: Be sure to check out how R defines a geometric random variable. 4. (10 points) Suppose the pdf for a continuous random variable X is given by 1≤x≤4, otherwise, f(x) = = √³/²x-³, 10, (a) Find E(X). (b) Find the CDF, F(x). Write your answer as a piecewise function. (c) Find P(X < 2). (d) Explain how your answer would differ if you were asked to find P(X ≤ 2). (e) Verify that your CDF is continuous at x=1 and x=4.