SYSEN536 HW3

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School

Pennsylvania State University, World Campus *

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Course

536

Subject

Industrial Engineering

Date

Feb 20, 2024

Type

xlsx

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Uploaded by CountSeaLionMaster1018

Problem 1 P(A and B) 12% 29% P(A) 41% P(B) 65% 35% P(B|A) 29.27% P(A|B) 18.46% 17.1% P(A and B ) P( B ) P( A | B )

Part a Beta for the exponential distribution PE(T<=15|Beta)=0.5 Beta Mean #NAME? b) PN(Y <=25 | μ, σ) = 0.25 PN(Y <=125 | μ, σ) = 0.75 Mean μ #NAME? 74.13 c) Pr(Y <= 15 |Min, MostLikely, Max)= 0.15, 15 Pr(Y <= 50 |Min, MostLikely, Max)= 0.50 50 The parameters μ and σ for a normal distribution St. Deviation σ Find the Min, Most Likely, and Max for the triangular distribution given: Pr(Y <= 15 |Min, MostLikely, Max)= 0.15,

Pr(Y > 95 |Min, MostLikely, Max)= 0.05. 95 Mean Estimation 53.33 Mean 48.19 d) Find the parameter value a1 and a2 for the Beta Distribution PB(Q<=0.3|a1,a2)=0.05 PB(Q<=0.5|a1,a2)=0.25 Alpha 1 3.674952 Alpha 2 2.169143 Mean #NAME?

a) No. of defective No.of Boxes 0 68 1 27 2 3 3 2 AIC Poisson 164.8122 BIC Poisson = 167.3 The Poisson is the best fitting as both AIC and BIC fittings. The m roughly amounting to 12 bulbs i

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