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- Let X1, . . . , Xn i.i.d. U([θ1, θ2]), i.e., X1, . . . , Xn are independent and follow a uniform distribution on the interval [θ1, θ2] for θ1, θ2 ∈ R and θ1 < θ2. Find an estimator for θ1 and θ2 using the method of moments.If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameterLet X1,...,Xn be an iid sample from f(x | θ) = θ xθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
- Let X1,...,Xn be an iid sample from f(x | θ) = θxθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θSuppose X1, . . . , Xn are i.i.d. from a continuous distribution with p.d.f. fθ(x) = 1/θ if 0 ≤ x ≤ θ, where θ > 0 is an unknown parameter. (a) Find E(X1) (b) Find the MME for θ. (c) Compute the variance of your MME from part (a).For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x=6.3, y=6.0, r=−0.228, P-value=0.111, and y=7.81−0.280x. Find the best predicted value of y(attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=5. Use a 0.10 significance level. The best predicted value of ywhen x=5 is nothing. (Round to one decimal place as needed.)
- For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x=6.3, y=6.0, r=−0.264, P-value=0.063, and y=7.92−0.304x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=4. Use a 0.01 significance level. The best predicted value of y when x=4 is __ (Round to one decimal place as needed.)The average normal daily temperature ( in degree Celsius) and the corresponding average monthly precipitation( in inches ) for the month of June are shown below for seven randomly selected cities. Compute for the value of r, complete the table with the needed information. Temperature(x) 30 27 28 32 27 23 18 Precipitation(y) 3.4 1.8 3.5 3.6 3.7 1.5 0.2For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x=6.3, y=5.9, r=−0.256, P-value=0.073, and y=7.73−0.285x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=6. Use a 0.01 significance level. The best predicted value of y when x=6 is?
- Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 8, x = 114.6, s1 = 5.03, n = 8, y = 129.3, and s2 = 5.38. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.) ,For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x=6.4, y=6.0, r=−0.211, P-value=0.142, and y=7.65−0.253x. Find the best predicted value of y(attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=5. Use a 0.10 significance level.
