Let X and Y have bivariate normal distribution with parameters:x = 5, y = 10, ox²=1, oy²=25 and Corr (X, Y) = p.(a) If p>0, find p when P (4

Answered: Let X and Y have bivariate normal…

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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Let X and Y have a bivariate normal distribution with μ = 70, X Find (a) E(Y|X= 76) (b) Var(Y | X= 76) (c) P (Y≤ 861X=76) 0²: X = 100, = 80, My o² = 169, and p=5/13.
Let Y, and Y, have a bivariate normal distribution. The marginal distribution of Y, is normal with mean u, and variance o, f(y1) = 20í ,-0 < yı < ∞, V2no, Calculate the marginal distribution of f (y2).
3. Find the boundary that corresponds the the probability for the standard normal distribution. (a) P(z< zo) = 0.8203 (b) P(zo < z) = 0.8997 4. Find the boundary that corresponds the the probability for the normal distribution. (a) P(x < xo) = 0.8203 when µ„ = 25 and op = 6.5 (b) P(yo < y) = 0.8997 when ly = 25 and oy = 6.5
E [X] = 4 and In X follows a normal distribution with a variance of 3. Express the value of E [min (X - 4, 1)] as the cumulative distribution function for the standard normal distribution.
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Find the equation of the normal line tola curve y= at (26.3, -100.7) 2+1 Select one: Oa 26.30000 x+1.00166y (7456703)-0 Ob.x+100166y+(127.16703)-0 Oc x+100166y-(7456703B) -0 Od 100.70000 x+1.00166 (/456703) -0 Oe answers not in the choices
5. Assume you are shooting at a target centred at the origin (0,0), but bullets land at a random point with horizontal (X) and vertical (Y) coordinates following in- dependent standard Normal (0,1) distributions. Define the distance from the tar- get to be D = VX²+Y². For independent standard Normals, we already know that X? - x²(1) = Gamma(1/2,1/2) and X² + Y² ~ x²(2) = Gamma(1, 1/2). Y /D %3D (a) Find the probability that a bullet lands in the top right quadrant. (Hint: You don't need to calculate any integrals.) (b) Find the conditional probability that a bullet lands more than 1 unit away from the centre (D > 1), given Y = X, i.e. the bullet lands on the identity line; express the probability as a function of the standard Normal CDF ¤(·). (c) Find the CDF of X² + Y² in closed form. (d) Find the probability that a bullet lands more than 1 unit away from the centre, P(D> 1). (e) Find the CDF of D based on the CDF of X? + Y². (f) Use your answer in the previous part to find the PDF of…
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Let X and Y be independent standard normal variates. Obtain the m.g.f. of XY.
Let W ~ Gamma(100, 3.4). (a) Give the exact value of P(1.5 < W < 5.0) (b) Give the approximate value of P(1.5 < W < 5.0) using normal approximation

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Let X and Y have bivariate normal distribution with parameters Hx = 5, y = 10, ox²=1, oy²=25 and Corr (X, Y) = p. (a) If p>0, find p when P (4