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Unformatted text preview: May mm are regardbd as four iudbpcctdcnt random variabibs with Common cumulative distribution dust ht A abmpany agrbbs tta ﬂCCEp’L Lb: highest of four sealed bids bit a property. The four bids function Which bfth fbilbwing IEPFESEE‘II’S the cxpectad valid: Uftbc accepted bid? {All (3} 1 F(x}=—[1+sinﬁ.t) 2 3!} :r J xcosm: {it 31']
1 H: I :
Ellzﬂ+ﬁiﬂﬁle tit 51': — x l+sinrrx 1bit
1534.! i ) 5?! {D} 1'~I:destsx[:1+sin Hf air {E} ‘1 :In'! I Hi 1
7st: I xCDSFrxﬂiSint'rx} tit
‘* 3:: ID forini
2 Cr: arse J 1i]. Two life lusuranee pelieles, each with edeath beneﬁt {if lilﬂﬂﬂ' and a onetime premium
of SUD, are said it} a eeuple, one for each persuh. The policies will Eltpire at the end of
the tenth year. The probability that only the wife will survive at least ten years is 0.015,
the pl'ﬂlitabllil‘j' that only the husband will survive at least ten years is IIJJJL and the prﬂbabllity that both of them will survive at least ten years is 0.96 . What is the expected exeess of premiums ever elelms, given that the husband survives at least ten years? (A) 350
{E} 335
(C) as?
{m are
(E) 39?
Mar we; is Caurse i 1?. An auto insurance company insures an automobile Watﬂl 15,000 for one year under a
policy with n 1,000 deduotihto. During the polio},r year more is e 0.04 chance of partial
damage. to the ear and n 0.02 chance of a total toss of the car. If there is partial damage to the oar, the amouothf damage (in thousands] follows 2: distribution with densitj,r function 0.5003 2“” for 0 c: x :15
0 otherwise. fEI)={ What is the expected claim payment? {A} 32o {B} see
1 (o) 352
(o) 330
:1 {E} see
1
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1
1
J
J
J .May zoo; 23 Course!
'1 JLJL_J[_III._.JL_£LJ LHJL_]L__IL_JI_I' J
1
'1
‘1
1
‘1 23. May mm A h05pital receive.5 H5 ofits ﬂu vaccine shipmanls from Company X and the remaindar
of its shipments fmm DLhEF companies. Each shipment contains a very large number at" vatcinc vials. For Campanyx’s shipmants, 10% afﬁne vials an: inaffeciix’e. For awry othar company,
2% of the vials arr: ineffcctivc. The: hospital tests 31] randomly selectad viaﬁs fmrn a shipment and finds that ﬁne vial is iusffecaive. Why “2 ~51: probability that this shipment cam: from Campan'f X ‘? {A}
{E}
{C}
{D}
ICE} 0.10
9.14
4137
0.153 {136 25' Course I 1?. Claim amounts for wind damage to inaured hemes are independent rand em variables J._£ with common deusit‘gr funetien l._E 3 —, fﬂrxbl f {I} = x"
E! uLherwIsc where :r: is the amount of a claim in mausanda. Suppose 3 such claims will be made. “J L_.J L._I _ What is the expected value efthe larges: of the three claims?
J
J {A} 2025
[ID _! [B] 2?
" {CJ 3233‘.
“t {D} 33?:3
...'I [E] 456D
1 May 2M! 33 [lemme I I L__l L—.J L.—.—_l In—._J II—l plan, the individual employees may choose exactly two of the supplementary coverages 3., E, and C, or they may choose no supplementary coverage. The proportions of the company's employees that choose coverages A, E, and C are respectively. Determine the probability that a randomly chosen Employee will choose no supplementary coverage. 3 1.
{A}
{E}
'33}
(DJ
{5}
May soar 4.1
144 NIH 9?
141 Fm insurer offers a health plan to the employees of a large company. As part of this . and LrJfr—I 12' Course l 35. The warranty an a machine Speciﬁﬂs that it will he ranianad at failure at aga 4, whichavcr nccun: ﬁrst. The machine's age at failuaa, X, has danait},r function 1
fix] = E
t} fhrDcxaﬁ ntht: rwisa. Lct Y be the agc at" Lha machine at the him: of raptaaamant. Datamina the variance nf Y. {A}
{E}
{C}
{D}
{E} 1.3 1.4 1.? 2.1 15 4} Court: I '..—!L—_L _l '._.I L._.._.]L..Jl._.ll.__lL__.I L l_lL_.lL_.ll_Jl—ll—J 37". May Edd} .a'L tour operator has a bus that can accommodate 21] tourists. The operator knows that tourists mag,r not show up, so he sells 21 tickets. The probahiliht that an individual tourist will not Sllﬂw up is H.132, independent of all other tourists. Each ticket costs it}, and is nonrefundable if“ a tourist Fails to show up. It‘ a tourist shows up and a seat is not available, the tour operator has to pay IUD [ElCltcl‘ cost + 5') penalty} to the tourist. E‘fhat is the expected revenue of the tour opcmtor? (A) ass
{a} sac
{C} as?
to} sea
{E} 935 4'3 Cowae I LJLJLJLJQ I.___1t___.!l__lL__Jl._.Ji_ 39. May 2am An insurance eelrupah],r insures a large number efhumes. The Insured value, X, of a randomly selected heme is assumed to fellow a distribution with deusi’ql.r functIDr: Given that a randomly seieeted home is insured far at least 1.5, what is the probability ftxl={ that it is insured fer less than 2 '? {A}
(B)
{C}
[D]
{E} (LETS
{L534
5.11%
13.829 113E 33:” D 45 ferxbl uthe twise. Ca “rate” 1' ‘._._I. L—Jl I_l. t_t l___l l._._ll. l_l t_...l L_.J. [—1 L__tt. .l_'l_llt_._ill__‘l.L.._._l:l._'li_ 4]. May seat A public health researcher examines the medical records cf a gmup cf93? men who died in 1999 and discovers that 2149 cf the men died frcat causes related tc heart disease. Mcrecver, 31?. cf the 93? race had at least crte patent wile suffered from heart disease, and, of these 312 Inc]:1 192 died from causes related tc heart disease. Dctcmﬁne the rareﬁed11:1ilit}r that a man randtzlrttl],r Selected from this group died of causes related to heart disease. given that neither cf his parents suffered frcrn heart disease. {at} c. 1 I a
{a} 0.113.
(a), case
(a) cast
{a} data 45 Ccurre t ...
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