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- Help pleaseee tyyySuppose you have a joint distribution of x and y where • x has population mean ug and population variance o? • y has population mean ly and population variance o, and the population covariance between them is Ery. The population Pearson correlation is then given by Ery OxJy We collect n pairs of data, (X;, Yi), i = 1,.. , n. Each pair is an independent draw from this distribution. (a) Suppose we estimate our population covariance with n 1 (x; – Ha)(yi – µy). i=1 Is this an unbiased estimator of the population covariance? Show why or why not. (b) Suppose we estimate our correlation with (xi – Ha)(Yi – Hy) - n i=1 Ox0y Is this an unbiased estimator of the population correlation? Show why or why not. =WI12) A metal bar is heated, and then allowed to cool. Its temperature T (in °C) is found to be The time is in minutes. T=15+75e-0.25 t Find the time rate of change of temperature after 5.0 minutes. 13) The standard normal curve (sometimes called the bell curve) in statistics looks like: 1 -x² y = e 2 √2π Show that there are two inflection points at x = +1
- 5. Assume = 0.06 and let the force of mortality be given by 0.04, 0 < t < 20 { 0.05, 201.9.18. Find the mean and the variance of the distribution that has the cdf x <0 0The following sums have been obtained from 100 observation pairs : Ex = 12,500, Ex“ = 15, 85000, Ey = 8,000 Ey = 6,48100, Exy = 10, 07, 425. Find the regression equation of y on x. cowoossps oTQuestion 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ" (Υ - Y)2 Σ1(Y₁-Y)²¹ SxY √SXXSYY' where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)². R² = "XY =2. Write the equation of the normal line to the function: y = 6v2x – 1 at the point (2.5, 12). Express the equation in the form ax + by + c = 0Suppose that n= 195 I.I.d. observations for (Y, X;) yleld the following regression results: v= 32.68 + 67.55Xx, SER= 18.63, R = 0.84 (15.7) (12.5) Another researcher is interested in the same regression, but he makes an error when he enters the data into the regression: He enters each observation twice, so he has 390 observations (with observation 1 entered twice, observation 2 entered twice, and so forth). Which of the following eatimated parameters change result? (Check all that apply) O A. The estimated intercept and slope. O B. The R of the regression. Yc. The standard error of the regrussion (SER). YD. The standard errors of the estimated coefficients. Using the 390 observations, what results will be produced by his regression program? Ý= 32.68 + 67.55X, SER =.R = 0.84 (Round your responses to two decimal places)Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON