4.5-1Let X and Y have a bivariate normal distribution with parameters Hy=- 3, µ,=10, o2=25, o=9, and p=3/5.%3DComputea) P(-5 < X < 5).b) P(-5 < X < 5 | Y = 13).c) P(7 < Y < 16).d) P(7 < Y < 16| X = 2).

Answered: Image /qna-images/answer/231b8fc6-6dca-4546-b0bb-c07232b7549b.jpg

Answered: 4.5-1 Let X and Y have a bivariate…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. Let Y₁ 5)
9. Let X be a three dimensional normal with mean and covariance (0) H = Σ = 2 1 1 1 3 -1 1 -1 2 Set Y₁ = X₁ + X2 + X3 and Y2 = X1 + X3. Determine the conditional distribution of Y₁ given that Y₂ = 0
Let x¡, denote a series of n numbers {x;: i=1,2,..,n}: Assume that x; is drawn from a distribution that is N(ux, ož). Show that the sample mean x = E, xị has a variance of ož/n carefully stating any required assumptions i. 1 at each step. ii. Show that the sample mean is an unbiased estimator of ux.
b) i. Let Y be the mean of sample of size n from a normal distribution with mean μ and variance 100. Find n so that Pu-5<Ỹ < µ+5)= 0.954
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
16. Let X, X2 X, be a random sample from a normal distribution, X, N(6, 25), and denote by X and S2 the sample mean and sample variance. Use tables from Appendix C to find each of the following: (a) P[3 < X < T. (b) P[L860< 3(X-6)/S]. (c) PIS <319375]
Q1:B B. Let X and Y have a bivariate normal distribution with parameters u, = 3, ly = 1,0 = 16, o, = 25, %3! and p = Suppose that P(c,
A normal distribution has μ = 30 and σ = 5. (a) Find the z score corresponding to x = 25. (Enter an exact number.) (b) Find the z score corresponding to x = 44. (Enter a number.) (c) Find the raw score corresponding to z = −3. (Enter an exact number.) (d) Find the raw score corresponding to z = 1.5. (Enter a number.)
A,b,c,d.
3) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X < 70) c) The 95 th percentile
Q.4-52
roblem 1 If the population parameters are μ = 7 and σ = 1: a) Compute the z score for the lowest (x-4) and highest grade (x=10). (15 pts) -3 b) Compute the proportion of the normal distribution corresponds to z-score values greater than the highest grade. (10 pts) 7 = 7 0 σ = I X = 10 3 3.00

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4.5-1 Let X and Y have a bivariate normal distribution with parameters u= - 3, u,=10, o?=25, o=9, and p=3/5. Compute a) P(-5 < X < 5). b) P(-5 < X < 5 | Y = 13). c) P(7 < Y < 16).