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4. Let the joint pam. of X and ¥ be defined as 1 pe 1,2,3,4 few) = .2oy (9) Find marginal pans. of X. (b) Find marginal pant. of ¥ (6) Find P(X > ¥). (@) Find P(Y = 2x). * (6) Find P(X +¥ =3). (6) Are X and ¥ independent? Why or why not? (g) Find conditional distribution of XY 5. Find e for which this is « valid joint pd. S(zu)= 1+ zy), O21) ©) Pex en) (9 PUX-@ <5) @ Pia <6) et the jit pat of Yaad ¥ be fw) 2B, xe 23 ye 12 Find the marginal pms. of X and Y. ind for which this is ali joint pa, Slew)=de +29), 2012 yoL23 ‘An insurance company company sells an automobile policy with a deductible of one unit. Let X be the amount of the los having pn. 09, say {"e wr cis a constant Determine cand the expected valu ofthe amount the inmrance company mst av ‘Suppose that a school has 20 classes: 16 with 25 students in each, three with 100 students in each, ‘and one with 300 students, fora total of 1000 students. (0) What is average class size? (b) Select student randomly out ofthe 1000 students. Let the random variable X equal the size of ‘the class to whieh this student belongs, and define the pam.t. of X. (€) Find B(X), the expected value of X. Let and o? denote the mean and variance of the random variable X. Determine B[(X ~ p)/o] and BUX ~ w/o}. It is beloved that approximately 75% of American youth now have insurance due to the health care law. Suppose this is true, and let X equal the number of American youth in a random sample of 5 with private health insurance. (0) How is X distributed? (©) Find the probability that X is at last 10. (6) Find the probability that X is at most 10. (4) Find the probability that X is equal to 10. (6) Give the men, variance, nnd standard deviation of X. ‘An excellent free-throw shooter attempts several free throws until she misses. () Ip = 09 is her probability of making a free throw, what ‘miss on the 13th attempt or later? (b) If she continues shooting until she missus three, what is the probability that the third miss occurs fon the 30th attempt? the probability of having the frst A Doaseball team lows $100,000 foreach day it rains. Say X, the numberof days it rains in a month, thas» Poison distribution with mean 0:2. What is the expected los i the frst month? 
