Question

please answer all questions

Suppose you are interested in bidding on a parcel of land and you know that one other bidder is interested. The seller has announced that the highest bid will be accepted. The other competitor's bidding price for the land will vary evenly from $72,000 to $85,500. a) Let B be the competitor's bid for the parcel of land. What are the distribution and parameter(s) of B? b) What is expected value and standard deviation of the competitor's bid? c) What is the probability that the competitor's bid will be less than $80,000? d) What values mark the middle 50% of the competitor's bids? e) You and the competitor each put in a sealed bid (i.e. you do not know the competitor's bid and he does not know yours). Suppose that you bid $79,000. What is the probability that your bid will be accepted? (i.e. that yours will be higher than the competitor.) 1) The competitor has hinted that he will not go higher than $82,750. What is the probability that his actual bid is above $80,200?

Answer 1

I have assumed the distribution to be a continuous one as $82000.5 is larger than $82000 and hence the competitor can bid $82000.5.
1. Let x be the distribution for the competitor's biddin price for land. Then, Xn U (72000, 850500) a-) fx (2)= 1, acaso - b-a . Here 6-85500 and a272000 ey fx600) > 1 { 720003 X5 85500 85500-72000 13500 6.) E(X) = (x da > [x2 la 62a² 2 (6-a) 2(B-a) e bra *E(X) > 85500+12000 2 157500 $78750 b a b-a

E (X2) [ 23 Ja & x² dx a Cb-a) 3cb-a) 2 63 93 3 (6.a) (b-a) (6² abta² 3Cb-a) b²+ ab + a² 3 '.V(xa 6²ab4a2 to b'rab + a2 (be bra)" 3 & b ² + ab + a2 (6²+2ab+a 2) 2 Gb + a4a6+4a²-3b²-6ab-3a2 a 6² 2ab + a2 12. > C6-02 1 2

12 .V(K), (85500 - 72000) ? 2 2 15,187,500 "SD (X) = √v (X) = /15187500 >$3897.11 e.) P[ *< $800001 80000 1 daa 8000 , 0.5926. 72000 13500 13500 d.) P[ X < x] 2 0.5 Ć I d220.5 13500 7200 13500 dazo sy 2 - 72000 2 6750 => 212 $78750

e) PL X5 79000] = 79000 s dx 2 7000 , 0.5185 72000 13500 13500 f.) P[ X > 80 200|X882750] > P[X780200 n x382750] P[X582750] z P[80200< x < 82750] PEXS 827307 82750 80200 13500 da 82750 I da 25050 13500 10750 13500 20.2372 72000 13500