HW7 - (a c satisfies P(8 or > 5cla = 5 = 0.1 P X19(n-a2 > 19 X52 2 1)82(5C)2 or or 19c2 0.1 = Xf9,0.1= 27.203 = 1.197 5 so c = J27.203 19(b Since s =

# HW7 - (a c satisfies P(8 or > 5cla = 5 = 0.1 P X19(n-a2 >...

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- 85- 5.31 - . P (8 > 5cla = 5) = 0.1 19c2 = Xf9,0.1 = 27.203, P ( 2 _ (n - 1)82 19 X (5C)2) _ X19 - 2 > 52 - 0.1 a . or so or or c = J27.203 = 1.197. 19 (b) Since s = 7.5 > 5c = 5.983, the engineer would conclude that a> 5. (a) c satisfies P( -tS,.10 ~ Ts ~ tS,.lO) = 0.80, P( -tS,.05 ~ Ts ~ ts,.od = 0.94, P(tS,.05 ~ Ts ~ ts,.od = 0.04, P(Ts > -tS,.05) = 0.95. 5.24 t5,0.05 = 2.015, tlO,0.10 = 1.372, tl~,0.90 = -1.372, and t20,0.01 = 2.528. 5.25 (a) a = 1.812, b = -2.764, c = 1.372, and d = 2.228. (b) a = tlO,0.05, b = tlO,0.99 = -tlO,O.Ol, c = tl0,0.10, and d = tlO,0.025. 5.26 5.29 irO,1O,0.025 = 3.72, irO,1O,0.975 = 1/3.72 = 0.27, 15,10,0.10 = 2.52, 15,10,0.90 = 1/110,5,0.10 =•• and irO,5,0.90 = 1/2.52 = 0.40. 5.30 (a) a = 2.85, b = 0.176, c = 2.24, d = 0.24, and e = 3.51. (b) a = IS,12,0.05, b = fs,12,0.99 = 1/ ir2,S,0.01lc = fs,12,0.1O, d = IS,12,0.975 = 1/112,s.c.rm- •••• e = fs,12,0.025' 5.28 (a) 100 random samples were generated. (b) From the simulation, t4,0.25 = -0.554, t4,0.5 = 0.164, and t4,0.90 = 1.809. TIle eIIK& values are t4,0.25 = -0.741, t4,0.5 = 0, and t4,0.90 = 1.533. 5.27 (a) 100 random samples were generated. (b) From the simulation, t4,0.25 = -0.656, t4,0.5 = 0.081, and t4,0.90 = 2.065. I1Ie...a values are t4,0.25 = -0.741, t4,0.5 = 0, and t4,0.90 = 1.533. Solutions for Section 5.4 Solutions for Section 5.3

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a = P (F1I1,1I2 \$ 1111,112,1-0;) = P (_p,1 \$ 1111,112,1-01) Jl2,1I1 = P (FII2,1I1 ~ f 1 ) 111,112,1-01 Hence, 1112,111,01 = 1/1111,112,1-01' 5.32 1- a = P ( -tll,0I/2 ~ TII \$ tll,0I/2) = P (T; ~ t~,01/2) = P (F1,1I \$ t~,01/2) - t2 Hence, 11,11,01 - 11,01/2' 5.33 (82)(n1-1)S?[1]) 4 [~~ = ~]) For (n1 = 7, n2 = 5), P (~~ > 4) = P (FS,4 > 6)::::: 0.05 For (n1 = 13, n2 = 7), P (~~ > 4) = P(F12,S > 8)::::: 0.01 For (n1 = 9, n2 = 16), P (~ > 4) = P (FS,15 > 2.133) ::::: 0.10 Solutions for Section 5.5 5.34 Since the rth order statistic in a random sample of size n from a U[O, 1] distribution has beta distribution with parameters r and n - r + 1, Xmin '" Beta(l, 9), Xmax "" Beta(92 and X = X(O.5) '" Beta(5, 5).
• Spring '08
• SAWYER
• Mean squared error, xmin, xmax

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