1. If the joint probability is given by:a +yf(r, y) =30for r = 0, 1, 2, 3; y = 0, 1, 2,Find:(a) P(X < 2, Y = 1);(b) P(X > 2, Y< 1);(c) P(X>Y );(d) P(X + Y = 4).

As per our guidelines,we are allowed to answer first three sub-parts only. Thanks a) P(X≤2,Y=1) =…

Answered: 1. If the joint probability is given…

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. Let X and Y be random variables, and let a and b be constants. (a) Starting from the definition of covariance, show that Cov(aX,Y) = a Cov(X,Y). You may find it helpful to remember that if EX = µx, then EaX = aux. (b) Show that Cov(X + b, Y) = Cov(X,Y). Now let X, Y, Z be independent random variables with common variance o?. (c) Find the value of Corr(2X – 3Y + 4, 2Y – Z – 1). You may use any facts about covariance from - the notes, including those from parts (a) and (b) of this question, provided you state them clearly.
4
X and Y are independent, X ~ U (0, 1) and Y U (0, 1). Calculate the probability P(X+Y<1.5).
Assume b, c are independent random variables with uniform distribution on the interval [-L, L), where L e R'. Find the probability that the solutions of the quadratic equation x? + bx + c= 0 are real. What happens when L → +0?
Given the situation where the failure of a structure is given according to the following condition: DeadLoad + LiveLoad is greater than the Resistance If the variables are acting independently from each other, and each one is normally distributed as follows: DeadLoad ~ N(100,25), LiveLoad ~ N(150,50) and Resistance ~ N(300,20). Compute the failure probability of the structure.
If X and Y are independent RVs, each following N (0, 3), what is the probability that the point (X, Y) lies between the lines 3X + 4Y = 5 and 3X + 4Y = 10?
Q3: Suppose the joint probability function of X and Y is given by x= 5, y = 0 7 x= 5, y = 3 7 x = 5, y = 4 P (x,y)- *= 8, y = 0 7 x= 8, y = 4 else Compute E(X|Y-0), E(X|Y 4), E(X|Y=3)
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Q2) The joint probability function of two discrete random variables X and Y is given by fx.y) = c(2x+y),where x and y can assume all integers such that 0< x<2, 0< y<3,and f(x.y) = 0 otherwise. (a) Find the value of the constant c (b) Cov (X, Y), (c) p.
Use a Venn diagram. Let P(Z) = 0.44, P(Y) = 0.28, and P(Z U Y) = 0.57. Find each probability. (a) P (Z'n Y') (b) P(Z'U Y) (c) P (Z' U Y) (d) P (Zn Y')
If the joint probability is given by:f(x,y) = (2x + 2y)/40, for x = 0, 1, 2, 3; y = 0, 1, 2, 3 a.) Find P(X>Y ): b.) Find P(X > 2, Y ≤ 1): c.) Is the equation valid? YES OR NO d.) Find P(X ≤ 2, Y = 1): e.) Find P(X + Y = 4):

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1. If the joint probability is given by: x+ y f(x, y) = 30 for r = 0,1,2, 3; y = 0, 1, 2, Find: (a) P(X s 2, Y = 1); (b) P(X > 2, Ys 1); (c) P(X>Y ); (d) P(X + Y = 4).