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- Use 7.3Let X1, X2, X3, X4 have the joint probability density functionf(x1, x2, x3, x4) = (24e−(x1+x2+x3+x4), 0 < x1, x2, x3, x4 < ∞0, elsewhereLet Y1 = X1, Y2 = X2 − X1, Y3 = X3 − X2, Y4 = X4 − X3.(i) Using the change of variable technique, find the joint probability density functionof Y1, Y2, Y3, Y4(ii) Find the conditional distribution of Y4 given Y1, Y2, Y3Suppose Var(X) = 36, Var(Y) = 42, and X and Y are independent. What is Var(.25X + .75Y)? Suppose Var(X) = 63, Var(Y) = 87, and X and Y are independent. What is Var(.79X + .21Y)? Suppose that Var(X) = 907.96, Var(X) = 10219.44, and Cov(X,Y) = 2694.59. What is Var(.33X + .67Y)?
- how close to -6 we have to take x so that 1/ (x+6)2 > 100 ??An electronics retailer wants to send codes for $10 off a pair of headphones to the subscribers of its e-mail list. The coupon code will have two letters followed by three digits. The letters A , B , C , and D and the digits 6 and 9 will not be used. So, there are 22 letters and 8 digits that will be used. Assume that the letters and digits can be repeated. How many such coupon codes can be generated? couponcodesA clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (36 + J )C - 2C 2 and the profits of the jeweler will be (30 + C )J - 2J 2. The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be Group of answer choices $17. $34. $51. $8.50. $25.50.
- Using the random variables X and Y from Table 2.2, consider two new random variables W = 4 + 8X and V = 11 - 2Y. Compute (a) E(W) and E(V); (b) J2W and J2V; and (c) JWV and corr(W, V).Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election. Sleaze’s share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S = 100N/(N + 1), where N is the number of ads. If each ad costs $4,900 approximately how many ads should Jiffy-Pol buy in order to maximize its profits? A) 2,853. B) 1428. C)98 D) 477.(d) Suppose that the satifaction received from a number of rides taken on a roller coaster (2x+1Y 0.5 is given by the function S(x) = 200() where S is the satisfaction received and x is the number of rides taken. (i) Find the rate at which the satisfaction changes with respect to the number of rides taken.
- A bakery would like you to recommend how many loaves of its famous marble rye bread to bake at the beginning of the day. Each loaf costs the bakery $2.00 and can be sold for $7.00. Leftover loaves at the end of each day are donated to charity. Research has shown that the probabilities for demands of 25, 50, and 75 loaves are 30%, 20%, and 50%, respectively. Make a recommendation for the bakery to bake 25, 50, or 75 loaves each morning. Find the expected monetary value when baking 25 loaves. EMV=$(Type an integer or a decimal.) Find the expected monetary value when baking 50 loaves. EMV = $(Type an integer or a decimal.) Find the expected monetary value when baking 75 loaves. EMV = $ (Type an integer or a decimal.) Make a recommendation for the bakery to bake 25, 50, or 75 loaves each morning. The bakery should bake loaves of bread every morning. O 25 50 75 EUse bordered determinants to check the following functions for quasiconcavity and quasiconvexity: a) Z=−x2−y2(x,y>0) b) Z=−(x+1)2−(y+2)2(x,y>0).Given the functional relationship: y = 14x5/x2 find the value of y when x = 1.5