Problem 3. Suppose a point (X, Y) is chosen at random from a disk S = {(x, y) : (x − 1)² + (y + 2)² ≤ 9}.(A) Determine the conditional PDF of Y given X.(B) Compute P(Y > 0: X = 2).

A point (X, Y) is chosen at random from a disk

Answered: Problem 3. Suppose a point (X, Y) is…

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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2. Suppose that z is a function of r and y, and F(xz - y², xy - 2², yz - ²) = 0. Calculate and (Hint: Since F = 0, then dF = 0. Use a proper change of variables and chain rule to proceed)
Q. 2: Let fx) = JX Sx- 3 %3D ー1 (x) f puy -o b- Find the domain and range f f(x)
4. Find the optium path for f=xy³ from (2, 1, 2)
2. Let P denote the path that goes in straight lines from (1,1,1) to (-1,-1,1) to (-1,-1,-1) to (1,1,-1) and then back to (1,1, 1). 2xyz+z el +2 x²z+sin(z) Compute fp F. dr, where F(x, y, z) = P
Suppose f, f', g, and g' have the following values: 1 2 3 4 f(x) 8 2 1 -8 f'(x) g(x) 10 -7 - 2 6 -6 – 253 - 252 - 246 - 248 - 262 - 64 56 14 - 15 23 (2),6 At the half-time show for a Milwaukee College football game, a balloon will travel along a path with equation z + y = f(x)g(x) and will be released at the point where x = 2. To ensure the safety of the crowd, Sophia needs the equation of the line tangent to the graph of 2° + y° = f(x)g(x) at x = 2 For this question, if you choose to use decimals, be sure that you round your numbers to at least 4 decimal places. The equation of the tangent line is:
2. Consider the function: ;0sxs1 fx(x) = { c(2 - x) ; 1 2 ... ... Fx(x) ... ... (c) What is the mean (expected value) of Xx? (d) What is the variance of X? A median of X is a value m that splits the probability in half: 1 P(X s m) = P (X > m) = In this problem X has one such m. Show that this median is the same as the mean of X. Does it always have to be (i.e., for other R.V.s)?
from ( 0,1) to (2,5)**

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Problem 3. Suppose a point (X, Y) is chosen at random from a disk S = {(x, y) : (x − 1)² + (y + 2)² ≤ 9}. (A) Determine the conditional PDF of Y given X. (B) Compute P(Y > 0: X=2).