Please show all your work attached is formula sheet 2. Suppose you are to choose among two suppliers of a certain chemical solution used in paint production.The production process yields the best results if the solution has 12% concentration. Both suppliersare capable of producing the desired concentration, however there is naturally occurring random fluc-tuations in the end product.Your analysis of sales samples provided concludes that the solution concentration from Supplier 1follows a distribution with the density function fi(x) = for 0 < a < 24, whereas the solution2x324concentration from Supplier 2 follows distribution with the probability density function f2(x) =for 0 Axloms of ProbablityAlso Note1. P(8)-12. For any event E, 0S P(E)s1For any two events A and B,P(A) - P(AN B) + P(ANB)3. For any two mutually exclusive events,andP(EUF) - P(E) + P(F)P(AN B) - P(A|B)P(B).Addition RuleEvents A and B are Independent if:P(EUF) = P(E) + P(F) - P(En F)P(A|B) = P(A)Conditional ProbablityorP(B|A) -P(ANB) - P(A)P(B).PLAN)Bayes' Theorem:Total Probablity RuleP(A|B)P(B)P(B|A) = PLALBPB) + P(AB)P(B")P(A) - P(A|B)P(B) + P(A|B')P(B')Similarly,Similarly,P(A) -P(A|E,)P(E)) + P(A|E)P(E)+...+ P(A|E)P(E)P(B|E)P(E)P(E|B) - PIBIE PE) + P(BE PE)+...+ P(B\E)P(E.)Probability Mass and Density FunctionsIf X is a discrete r.v:Cumulative Distribution Function• F(z) = P(X sz)P(X = 2) = f(z)• lim,- F() -0Es(2) =1 (total probability)• lim,e F(z) = 1If X is a continuous r.v.:P(X = z) = 0• F(z) = " /(v)dy if X is a contimuous r.v.S(2)dz =1 (total probability)• F(z) = E,sz f(z) if X is a discrete r.v.• P(a < X Sb) - F(b) – F(a)Expected Value and VarianceExpected Value of a Function of a RV• E[X) = E, z/(z) if X is a discrete r.v.• E[h(X)] =E. h(x)f(x) if X is a discrete r.v.• Eh(X)) = h(z)/(z)dz if X is a continu-• E[X] = z/(z)dr if X is a continuous r.v.ous r.v.• Var(X) = E[Xx] – E[X]?• E(aX + 6) = aEX] + 6• Var(aX + b) = a?Var(X)%3D• Var(X) = E[(X - E[X])?]Derivatives and Integrals of Common Functions• = aeade• Sea" dz =• Sre*dr = e"I- fe*dz = ze" - e (using integration by parts)dinz• S !dz = In(z)Common Discrete Distributions• X - Bernoulli(p),if z = 1;f(z) =|1-p ifz 0' EX] = p, Var(X) = p(1 – p).• X- Geometric(p),f(2) = (1– p)--'p, z E {1,2,..}, E[X] = }, Var(X) = .Geometric Series: Eg = , for 0 < q < 1• X - Binomial(n, p),f(z) = (E) (1– p)"-p*, I € {0, 1,.., n},E[X] = np, Var(X) = mp(1 – p).%3D• X- Negative Binomial(r, p),f(z) = ()(1 – p)*-"p", E[X] = ;, 1 € {r,r+1,..}, Var(X) = p),%3D• X - Hypergeometric(n, M, N),f(z) =,E[X] = n, Var(X) = N=n(1-).%3D• X ~ Poisson(At),f(z) = A0", z e {0, 1, .}, E[X] = At, Var(X) = At.Common Continuous Distributions• X - Exponential(A),f(z) = de-A, z E [0, 00) E[X] = }, Var(X)= .• X- Erlang(r, A),f(z) = A' , zE (0, 00), E[X] = 5, Var(X) = .Suppose that Duke Energy mu

It is given that number of suppliers is 2 and density function f1(X) = 110 for 0≤X≤10f2(X) =…

2. Suppose you are to choose among two suppliers of a certain chemical solution used in paint production. The production process yields the best results if the solution has 12% concentration. Both suppliers are capable of producing the desired concentration, however there is naturally occurring random fluc- tuations in the end product. Your analysis of sales samples provided concludes that the solution concentration from Supplier 1 follows a distribution with the density function fi(r) = for 0 < a < 24, whereas the solution concentration from Supplier 2 follows distribution with the probability density function f2(x) = for 0

2. Suppose you are to choose among two suppliers of a certain chemical solution used in paint production. The production process yields the best results if the solution has 12% concentration. Both suppliers are capable of producing the desired concentration, however there is naturally occurring random fluc- tuations in the end product. Your analysis of sales samples provided concludes that the solution concentration from Supplier 1 follows a distribution with the density function fi(r) = for 0 < a < 24, whereas the solution concentration from Supplier 2 follows distribution with the probability density function f2(x) = for 0

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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