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HOMEWORK 1 SOLUTIONS
Question 3. a) x! = x! + x! + x! + x! + x! + x! ! !!! b) y! = y! + y! + y! + y! + y! ! !!! c) !!!! = !!!! + !!!! + !!!! ! !!! d) !!!! = !!!! + !!!! + !!!! + !!!! + !!!! + !!!! + !!!! + !!!! ! !!! e) !!^!^ = !!^!^ + !!^!^ + !!^!^ + !!^!^ + !!^! ! !!! f) !! + !! = !! + !! + !! + !! + !! + !! + (!! + !!) ! !!! Question 3.70: x! = 4 , x! = โ 2 , x! = 3 , x! = โ 1 , y! = 5 , y! = โ 2 , y! = 4 , y! = โ 1 a) x! = 4 + โ 2 + 3 + โ 1 = 4 ! !!! b) !! = 5 + โ 2 + 4 + โ 1 = 6 ! !!! c) !!^!^ = 4!^ + โ 2!^ + 3!^ + โ 1!^ = 16 + 4 + 9 + 1 = 30 ! !!! d) !!^!^ = 5!^ + โ 2!^ + 4!^ + โ 1!^ = 25 + 4 + 16 + 1 = 46 ! !!! e) !!!! = 4 5 + โ 2 โ 2 + 3 4 + โ 1 โ 1 = 20 + 4 + 12 + 1 = 37 ! !!!
Question 4. !! โ! (! โ !)! 7 -ยญโ1.5 2. 8 -ยญโ0.5 0. 4 -ยญโ4.5 20. 11 +2.5 6. 13 +4.5 20. 15 +6.5 42. 6 -ยญโ2.5 6. 4 -ยญโ4.5 20. 68 0.0 118. ! =
! !
Question 4.10 (a) !! โ! (! โ !)! 8.96 +0.01 0. 8.92 -ยญโ0.03 0. 8.98 +0.03 0. 8.96 +0.01 0. 8.93 -ยญโ0.02 0. 44.75 0.0 0. ! =
! ! โ 1
Question 4.12 (b) !! โ! (! โ !)! 13 -ยญโ 12. 7 161. 5 -ยญโ 20. 7 428. 26 +0. 3 0. 09 41 + 15. 3 234. 57 + 31. 3 979. 2 -ยญโ 23. 7 56 1. 25 -ยญโ0. 7 0. 49 10 -ยญโ 15. 7 246. 60 + 34. 3 1176. 18 -ยญโ7.7 59. 257 0.0 3848 ! =
! ! โ 1
Note the standard deviation in part b is 100 times the standard deviation in part a. Review Exercise 12: Sample: X=22, 16, 20, 20, 15, 16, 12, 14, 16, 14, 11, 16 !) !"#$! =
22 โ 16!^ + 16 โ 16!^ + 20 โ 16!^ + 20 โ 16!^ + 15 โ 16!^ + 16 โ 16!
+ 12 โ 16!^ + ( 14 โ 16 )!^ + ( 16 โ 16 )!^ + ( 14 โ 16 )!^ + ( 11 โ 16 )!^ + ( 16 โ 16 )!
Question 5. This is a question of permutation. There are 6 branches and 6 branch managers. Once a manager is selected from 6 managers and assigned to state one, for state two there are 5 managers left to select from. !"#$%&"! !": 6! = 6 โ 5 โ 4 โ 3 โ 2 โ 1 = 720 !"#$ Question 5. This is a question of counting. The travel agent can place orders in 5 ways: telephone, fax, email, priority email, and express mail carrier. The order can be confirmed by 3 ways: telephone, fax, and priority emails. Once he places order by telephone he can get confirmation in three ways. Next when he places the order using fax, he can get the confirmation in three ways as well, and so on. !"#$%&"' !": 5 โ 3 = 15 !"#$ Question 5. This is a question of counting. There are 10 soups or salads, 8 entrees, and 6 desserts. For example, for every option of soup or salad, he can choose one entree from 8 options and 1 dessert from 6 options. !"#$%&"' !": 10 โ 8 โ 6 = 480 Question 5. !)
Question 5. In a deck of cards there are 4 queens and 13 clubs. We are to draw cards from the deck without replacement. !) !"#$%$&'&() !" !"#$%&' 2 !"##$%. !"#$ !"#โ!"# !"#$%&"'"(), !"#$" !"#$!!! !"##$! โด !โ! !"#$%&' !"# !" !"#$%& !"! !"#$%&'(%"& !"#$%&'(. !"#$ 2 !"##$% !"#$ 4 !"##$% =
Question 5. Likely outcomes of flipping 4 coins: HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT. ! 0 โ!"# =
Question 5. A carton of 24 bulbs includes 2 defective bulbs. 2 bulbs are chosen at random. !) !โ!" !"! !"#$%&'(%"& !"#$%&'(.
