X and Y come from normal distributions
μx= 10, σx =5, μy=8, σy=4, ρ=0 X and Y come from normal distributions Calculate the...
Let X and Y have a bivariate normal distribution with parameters μX = 4, μY = 2, σX = 2, σY = 4, and ρ = 1/2. Find two different lines, a(x) and b(x), parallel to and equidistant from E(Y|x), such that P[a(x) < Y < b(x)|X = x] = 0.6827 for all real x.
Let X and Y have a bivariate normal distribution with parameters
μX = 10, σ2 X = 9, μY = 15, σ2 Y = 16, and ρ = 0. Find (a) P(13.6
< Y < 17.2). (b) E(Y | x). (c) Var(Y | x). (d) P(13.6 < Y
< 17.2 | X = 9.1).
4.5-8. Let X and Y have a bivariate normal distribution with parameters Ax-10, σ(-9, Ily-15, σǐ_ 16, and ρ O. Find (a) P(13.6< Y < 17.2)...
Let X and Y have the following joint distribution: X/Y 0 1 2 0 5/50 8/50 1/50 2 10/50 1/50 5/50 4 10/50 10/50 0 Further, suppose σx = √(1664/625), σy = √(3111/2500) a) Find Cov(X,Y) b) Find p(X,Y) c) Find Cov(1-X, 10+Y) d) p(1-X, 10+Y), Hint: use c and find Var[1-X], Var[10+Y]
Question 5 - Even More Fun With Bivariate Normal Distributions Let X and Y be independent normally distributed with mean x = 2 and μΥ--3 and standard deviations ơX-3 and ơY-5, respectively. Determine the following: (a) P(3X 6Y>15), (b) P(3X6Y<30) (c) Cov(X, Y) d) Verify (a) and (b) using R code, where for each case you generate a million X's and a million Y's and simulate the linear combination 3X 6Y. (e) Assume now that the random variables come from...
Suppose an x distribution has mean μ = 4. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81. (a) What is the value of the mean of each of the two x distributions? For n = 49, μ x = For n = 81, μ x = Suppose the heights of 18-year-old men are approximately normally distributed, with mean 70 inches and standard...
V. Hypothesis test and confidence intervals. 1. A sample (n) is taken at random from a population and produces (the sample) A = 1100, S = 200. Try the following hypothesis: If we assume the following size of sample n = 36 a, Is there evidence that the average μx is less than 1200? α = .10 H0: μx = 1200 H1: μx <1200 * For the previous test (item a) estimate the p-value * Determine the power of the...
7.70. Let X,...,x,; Y,., Y,; Z,..,Z, be respective independent random samples from three normal distributions N(u,a+ B, a) N(4-B+y,a), N(= a + y , a'). Find a point estimator for B that is based on X, Y, Z. Is this estimator unique? Why? If a is unknown, explain how to find a confidence interval for B.
7.70. Let X,...,x,; Y,., Y,; Z,..,Z, be respective independent random samples from three normal distributions N(u,a+ B, a) N(4-B+y,a), N(= a + y ,...
Problem #8 : A lamina with constant density ρ(r.))-5 occupies the region under the curve y-sin(m/8) from x-0 to x-8. Find the moments of inertia 4 and Enter the values of 4 and ly (in that order) into the answer box below, separated with a comma. Enter your answer symbolically, as in these examples Problem #8: Just save Submit Problem #8 for Grading Problem #8 | Attempt #1 | Attempt #2 Attempt #3 Attempt #4 Attempt #5 Your Answer: Your...
Given the following distributions: Normal (104) Triangular (4, 10, 16) Uniform (4, 16) find the probability that 6<x<8 for each of the distributions.
Please help solve the following with steps. Thank you!
3. Determine the center of mass of the paraboloid given by the surface -4-x2-y2 and (a) ρ(x, y, z)= 1 (b) pr, y,a) 5 0 if -z
3. Determine the center of mass of the paraboloid given by the surface -4-x2-y2 and (a) ρ(x, y, z)= 1 (b) pr, y,a) 5 0 if -z