# Donald has ordered a computer and a desk from 2

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Chapter 13 / Exercise 51
Nature of Mathematics
Smith
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15. Donald has ordered a computer and a desk from 2 different stores. Both items are to be delivered Tuesday. The probability that the computer will be delivered before noon is .6 and the probability that the desk will be delivered before noon is .8. If the probability that either the computer or the desk will be delivered before noon is .9, what is the probability that bothwill be delivered before noon?16. A distribution of grades in an introductory statistics class (where A = 4, B = 3, etc) is:X01234P(X).10.15.30.30?a.Find P(X= 4)b.Find P(1X3)c.Find the mean grade in this class.d.Find the standard deviation for the class grades.
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Chapter 13 / Exercise 51
Nature of Mathematics
Smith
Expert Verified
e.Find the lowest grade X0such that P(XX0)0.517. Suppose you have a distribution, X, with mean = 28 and standard deviation=2.1. Define anew random variable Y = 2X + 1.a.Find the mean of Y.b.Find the varianceof Y.c.Find the standard deviation of Y.d.Let W = X + X for X in the above problem. Find the varianceof W.
18. An appliance store is offering a special price on a complete set of kitchen appliances (refrigerator, oven, stove, dishwasher). A purchaser is offered a choice of manufacturer for each component:Refrigerator: Kenmore, GE, LG, WhirlpoolOven: KitchenAid, Samsung, Frigidaire, KenmoreStove: Electrolux, Hotpoint, GEDishwasher: Bosch, Silhouette, Premier, WhirlpoolUse the product rules to answer the following questions:a.In how many ways can one appliance of each type be selected?b.In how many ways can appliances be selected if none is to be Kenmore?
c.If someone randomly chooses their appliances, what is the probability that atleast one Kenmore component is chosen?19. Suppose that for events A and B, PA0.4,PB0.3, andPA B0.5.a.Compute PA| Bb.Are events A and B independent?20. Suppose that p(x,y)3xy, x= 1, 2, y= 1, 2, 3 is the joint pmf of Xand 39a.Create a contingency table for Xand Yy/x1214/397/3925/398/39310/3911/39b.Fill in the marginal values for the table.c.Find E[X], E[Y], and E[XYd.Find σX,σY, and cov(X,Ye.Determine if Xand Yare independent.Y..])