Please write by hand. I can’t understand sometimes when is writing in a computer. Please write by hand if not please do not respond. Attached will be the formula sheet 3. A volunteer is distributing flyers at a street corner for a comedy show. The number of people whoaccept a flyer as they pass by follows a Poisson distribution with the rate of µ = 4 people per hour.a) What is the probability that it takes more than 10 minutes for the volunteer to give out the firstflyer? eb) What is the expected number of flyers the volunteer would distribute in 6 hours?c) Suppose the volunteer has 3 flyers left. What is the exptected time it would take to run out offlyers?d) What is the probability that it would take more than an hour to distribute the last 3 flyers? 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

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accept a flyer as they pass by follows a Poisson distribution with the rate of u = 4 people per hour. a) What is the probability that it takes more than 10 minutes for the volunteer to give out the first flyer? b) What is the expected number of flyers the volunteer would distribute in 6 hours? c) Suppose the volunteer has 3 flyers left. What is the exptected time it would take to run out of flyers? d) What is the probability that it would take more than an hour to distribute the last 3 flyers?

accept a flyer as they pass by follows a Poisson distribution with the rate of u = 4 people per hour. a) What is the probability that it takes more than 10 minutes for the volunteer to give out the first flyer? b) What is the expected number of flyers the volunteer would distribute in 6 hours? c) Suppose the volunteer has 3 flyers left. What is the exptected time it would take to run out of flyers? d) What is the probability that it would take more than an hour to distribute the last 3 flyers?

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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