1. Determine the distribution of Y if its MGF is as follows: = cp[{{11+0²1²} exp inl a. my(t) =
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Q: Isn't here the standard deviation equal to 4, not 2, as the tutor wrote?
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What is the proof or solution that the MGF is
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- Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with ? = 4 and ? = 2. (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = V(X) = (b) Compute P(X ≤ 0.3). (Round your answer to four decimal places.)(c) Compute P(0.3 ≤ X ≤ 0.7). (Round your answer to four decimal places.)2- An expert estimates that the distribution parameter for durability times of parts produced with machine A in the factory is different from the distribution parameter for durability times of parts produced with machine B. Durability times of 4 parts produced from machine A and 4 parts produced from machine B are given below. Find the Mann-Whitney U value by using these data. a) 18 B) 6 NS) 16 D) 20 TO) 12The article “Wastewater Treatment Sludge as a Raw Material for the Production of Bacillus thuringiensis Based Biopesticides” (M. Tirado Montiel, R. Tyagi, and J. Valero, Water Research, 2001:3807–3816) presents measurements of total solids, in g/L, for seven sludge specimens. The results (rounded to the nearest gram) are 20, 5, 25, 43, 24, 21, and 32. Assume the distribution of total solids is approximately symmetric. a) Can you conclude that the mean concentration of total solids is greater than 14 g/L? Compute the appropriate test statistic and find the P-value. b) Can you conclude that the mean concentration of total solids is less than 30 g/L? Compute the appropriate test statistic and find the P-value. c) An environmental engineer claims that the mean concentration of total solids is equal to 18 g/L. Can you conclude that the claim is false?
- Suppose you know that Var(Z)=(k+1)E(Z) where k is 7. Determine the distribution of Z and find its parameter(s), explaining your argument carefully.In case of omitted variable bias, which of the following OLS assumption will be violated Group of answer choices (X,Y) are i.i.d. drawn from their joint distribution E(u|X)=0 There are no outliers for X and u. There is heteroskedasticity.For two random variables X and Y that follow exponential distributions with rates λ1 and λ2 respectively, calculate E(E(X|Y )) when the correlation between X and Y is ρ = 0.5.
- given normally distributed sample x=12 and s=3, use the Empirical Rule determine the upper and lower bounds to contain approximately 95% of your dataD.1.2 Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.13, and 9.8 liters. Use α 0.01 level of significance and assume that the distribution of contents is normal.Suppose that Z comes from standart normal disribution Given P(-k < Z < k ) =0.78 find k=?
- Find marginal distributions P(x) and P(y)Let X be a standard normal RV. Suppose Y = 2X+3 and Z = -X+6. a) Find the covariance between Y and Z b) Find the correlation coefficient between Y and ZSuppose you have a sample of size n for variables X and Y. The sample covariance of X and Y is Cov(X,Y) = 1,000, the sample standard deviation for X is Sx=20 and the sample standard deviation for Y is SY=75. What is the sample correlation coefficient, r?