Let Z1, Z2, ….be iid Normal(0; 1) rvs. Briefly explain how to use these rvs togenerate/construct a rv from the distributions in the list below. You may (and should) use the results fromearlier subproblems in order to solve later subproblems. You are not allowed to use the inverses of cdfs unlessyou can nd them in closed form (without integrals in the nal answer, i.e., of the Normal and Gammadistributions). Justify all your answers.1. Normal( mu = 1; sigma^squared= 4) 2. Chi squared with 1 degree of freedom 3.Chi squared distribution with n degrees of freedom4. Exponential(1)5. Uniform(0,1) 6. Exponential(B = 17) 7. Gamma(k; B= 19), k is a positive integer8. Cauchy distribution

 

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1. Let Z ∼ N (0, 1) (i.e. Z is a standard normal random variable.) Find the following probabilities using normal probability Table A.

(a) P(Z ≥ 0.98)

(b) P(−1.1 ≤ Z ≤ 1.37)

(c) P(0.7 ≤ Z ≤ 1.7)

(d) P(−1.4 ≤ Z) 

 

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Please answer the following question related to G-test, likelihood ratio test

Let Y1, Y2, Y5), be independent random variables with probability distributions that areNormal(m, (:2 = 1). That is, 1 — % (1;;- —Hi, )2B f(yé|#é)=m i=11253 _OO<,U"E<+OO The null hypothesisis of homogeneity states that all 3 random variables have the same Normaldistribution, i.e., Ho : p1 = pig = M3 = a. The alternative hypothesis states that at least 2 ofthe m’s are different. (a) Please derive G2, — for testing the null hypothesis of homogeneityversus the alternative hypothesis. Simplify as much as possible. (RECALL: 221:1 K; = n?) (b) What is the large sample probability distribution for G2 in this problem?

 

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Using PMBOK 5e, prepare five templates using specific quality tools that could be used to plan, assure, and control quality in the family garden scenario.

Choose from 1) flow charts, 2) check sheets, 3) Pareto diagrams, 4) histograms, 5) control charts, 6) scatter diagrams, 7) affinity diagrams, 8) process decision programs charts, 9) interrelationship digraphs, 10) tree diagrams, 11) prioritization matrices, 12) activity network diagrams, 13) matrix diagrams, 14) inspections, and 15) statistical sampling.

Not all of the tools are applicable or useful in the family garden scenario. Pick the tools you believe best apply to the project. This will require each of you to study each tool, understand how it is used, and whether or not it works with the family garden scenario.

• Attachment 1
• Attachment 2

 

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Letticia​ Garcia, an aggressive bond​ investor, is currently thinking about investing in a foreign​ (non-dollar-denominated) government bond. In​ particular, she’s looking at a Swiss government bond that matures in 15 years and carries a coupon of

8.81 %. The bond has a par value of 14,000 Swiss francs​ (CHF) and is currently trading at 105.05 ​(i.e., at 105.05​% of​ par). Letticia plans to hold the bond for a period of 1​ year, at which time she thinks it will be trading at 114.01. ​she’s anticipating a sharp decline in Swiss interest​ rates, which explains why she expects bond prices to move up. The current exchange rate is 1.61 ​CHF/U.S.$, but she expects that to fall to 1.24 ​CHF/U.S.$. Use the foreign investment total return formula to find the following information.

a. Ignoring the currency​ effect, find the​ bond’s total return​ (in its local​ currency).

b. Now find the total return on this bond in U.S. dollars. Did currency exchange rates affect the return in any​ way? Do you think this bond would make a good​ investment? Explain.

 

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