Question

Define the cumulative distribution function F(t) oft by F(t) = P(W <t). Shade the region consisting of each point (x, y) in which x > 0, and F(X) < y < 1. Compute the area of the shaded region.

Answer 1

given = 1-0.5 10-5 p(x=5) = 10es -> (120).s.co's)' + 210. + costs x be binomial with parameters n=1098=65 Anubhchip) The probability mass function is PP(x) = nexprea n10 p=0.5 I-P =0.5 Cons) co.s) => 252 coscosos =) 252 10.50 252. 1024 256 0.2460 P(x - )= = 10.2460 $135x26) = (x=3349 «*=w+p«=»)px=c) => 10 C, co si co.uju Hoca (0.5" (o.s) 0-4 16 cosyst 210 63 10-3 10 € flopscosyscossos + 100% CO-sjøco-5) -1 asa. 13 64 (0.5)

1 (120) - + 210. 250... 32 16 32 . +216. 64 -) 120 252 216 + 210 (०१५ न 1024 २०२५ 1624 792 104 ११ 128 10-1 - 0 1734 -'. (83693 167734 १(१.८3) = १९९0) + PCr : 1) Pex=251px-3) -) १०८, (0-5) (0-5) |10| (O•5)' (0-550 -1 10९ (0-55°C o •530-240, (65) (0-5303 →। 10t0.5/ 100030544sco.in (७.९)120 (5360.5) 7 > 45 120 1024 1024 1024 1024 > 16 1024 -) (61 On815 ... (43) = [0. I717

compate pex=5) 0.2460 computi p(3<356) 0.7734 compute CX =3) Lo @.1719

meinwa given normally distribution with $45,000 standand clication (G) = $10,000 less than $35,500 - P(x 4835,000 (X-11 < 33660-4) P 10ooo Prze 38540- 45000) Prz<-10000 = pz-1 using normal t-tare = 0.1587 pexc935000) - 16.1587 Between 83500 and & us, sro ::p(33770cxcusum) - p( 35600-4 = (35 uso-950m 1000 x-M 4500- 2 3500-4500 Lt, 10 000 EP (-10,000 cza 1o, o) 19,000 pel22<6) s pc<0)-PC2C-1) -) using normal q-tuste EOS- 0.1587 pe 35000 x 45700) = 3413

Between us out and 6000 peesoonex <GOWO) - prasto-, med Gorbo!) = 45000-4000 60000-4560 << 10000 1600 << 15000 lowo 10000 apce = prosz<1:5) =p(221.5j-peod using normal z-table 0.9332-0.5 4332 P90X7 x (GB) = Exactly $46000 PCXEU6D ) = p. 46000 =P(Z = 46, Oru - Usoov 10000 1000 ) 10000 pez=!0 Sp(2=0.1) using normal q-tasie 0.5398 ..pex= =96000) 10.5398 • Greater than $55,000 PC *> 65000) = perala 65000-e

p(z> 65000–45000 - pezs 20000 1000 - plaza) -la-pez<2) Using normal &- table 0.9772 0.0 228 ...pex765000) = 10.00 28 - less than $35000 10.1587 Between 83500 and susooo 0.3413 Between 845000 and 60000 0.4332 Exactly 846,000 0.5398 Greater than 865000 0.02 a 8