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10s418hw4nsol

# 10s418hw4nsol - P(X> 8 t|X>t = P(X>8 = exp-1/8*8 =...

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HW4 – MATH 418 Solutions (Need not submit) Ch. 5: 16, 19, 33, 35, 36: 16. P(X>50) = P( (X-40)/4 > (50-40)/4 ) =1 (2.5) 1 0.9938 = - Hence, ( P(X<50) )^10 = 0.9938^10 19. Let Z = (X-12)/2, then Z is a standard normal. Now, 0.10 = P(Z > (c-12)/2), but from table 5.1, P(Z<1.28) = 0.90 So, (c-12)/2 = 1.28 or c = 14.56 33. The distribution of exponential distribution has a property called “memory less”
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Unformatted text preview: P(X > 8+t|X>t) = P(X>8) = exp((-1/8)*8) = exp(-1) 35. 3 2 0.00025 0.02 ( ) 0.427 3 2 t t t dt t Î» = +-âˆ« (a) 50 0.353 40 ( ) 0.353; ( 50) 0.702 t dt P X e-= > = = âˆ« (b) 60 1.207 40 ( ) 1.207; ( 60) 0.3 t dt P X e-= > = = âˆ« 36. (a) 16 4 ( 2) 0.0183 P X e-â‰¥ = = (b) 2 2 0.4 1.4 4 4 (0.4 1.4) 0.611 P X e e--â‰¤ â‰¤ =-= (c) ( 2 | 1) 0.0235 P X X â‰¥ â‰¥ =...
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