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- ox² = 3, oy² = 5, oxy = 2, Z = 2Y - 4X – 2 a. Determine the variance of Z.Please Solve In 10minsX and Y are random variables that are the same normally distributed variables as in the previous problem. The Mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. You are now being told they are independent. Find the value of each requested parameter. The mean of T= - 3x + 20 is The mean of W= Y - X is The variance of D= X - 2Y is
- the random variable Y is such that : E(2Y+3)=6 and Var(2-3Y)=11 find E(Y^2)A and b solve onlyWe are trying to predict GPA (Y) using number of hours spent studying (X1) and gender (X2). Our indicator variable for gender with male as the base is: If = {1 if Female} {0 else Our model is Y = Bo + B1X1+ B2IF + 8 } What is the expected value of Y if gender is female? O HF = Bo + B1X1 O µF = 0 O HF = Bo + 1 O uF = Bo + B1X1 + B2
- Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)Solve number 2 onlySuppose X and Y are two independent variables with variance 1. Let Z = X+bY where b > 0. If Cor(Z, Y ) = 1/2, what is the value of b?
- Consider the following simple linear regression. iid Y = Po + B₁X + e, e~ N(0,02), i=1,..., n.Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S² = (₁-P) ². (d) Define V₁, a function of S1, that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for ofIf the random variable X as a mean of u and a variance of o2 what is the P((X-u)² < 20): O less that equal to 1/4 O greater than or equal to 3/4 cannot tell O equal to 5/4