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MATLAB: An Introduction with Applications
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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Every week, Alex receives $15 allowance from his parents. He usually spends most of it buying candy. In Alex's favorite candy store, M&M's are sold in bulk at $5 per pound, and Skittles are sold at $3 per pound. Let X and Y denote the weight of M&M's and Skittles Alex buys, respectively. Let the joint probability density function for (X, Y) be fx,y (x, y) = x²y, x > 0, y > 0, 5x + 3y < 15, O otherwise. From HW 7, we have fx (x) = x2 (3 – a)?, 0 <x < 3, 0 otherwise. fy (y) = Y(5 – y)³, 0 < y< 5, 0 otherwise. a. Are X and Y independent? O yes O no O not enough information to determine 提交答案| Tries 0/10 Find Cov(X,Y). Give your answer to 4 decimal places. 提交答案 Tries 0/5 b. Suppose we know that Alex purchased 2 pounds of Skittles. What is the probability that he bought less than 1 pound of M&M's? That is, find P(X < 1| Y=2). Give your answer to 4 decimal places. 提交答案| Tries 0/5 c. Suppose we know that Alex purchased more than 2 pounds of Skittles. What is the probability that he bought less than 1 pound of M&M's? That is, find P(X < 1 | Y > 2). Give your answer to 4 decimal places. 提交答案 Tries 0/5 d. Find E(X|Y=y). Enter a formula in the first box and two numbers in the second and third boxes corresponding the range of y. Use * for multiplication, / for division and ^ for power. For example, 12/15*y^2*(3-y)^3 means 12 y2(3-y)/15. E(X|Y=y) = < y < O otherwise. 提交答案 Tries 0/15 e. Suppose we know that Alex purchased 1 pound of M&M's. What is the probability that he bought more than 2 pounds of Skittles? That is, find P(Y > 2 | X=1). Give your answer to 2 decimal places. 提交答案| Tries 0/5 f. Suppose we know that Alex purchased 2 pounds of M&M's. What is the probability that he bought less than 1 pound of Skittles? That is, find P(Y < 1 | X=2). Give your answer to 2 decimal places. 提交答案 Tries 0/5 g. Find E(Y|X=x). Enter a formula in the first box and two numbers in the second and third boxes corresponding the range of x.
Transcribed Image Text:Every week, Alex receives $15 allowance from his parents. He usually spends most of it buying candy. In Alex's favorite candy store, M&M's are sold in bulk at $5 per pound, and Skittles are sold at $3 per pound. Let X and Y denote the weight of M&M's and Skittles Alex buys, respectively. Let the joint probability density function for (X, Y) be fx,y (x, y) = x²y, x > 0, y > 0, 5x + 3y < 15, O otherwise. From HW 7, we have fx (x) = x2 (3 – a)?, 0 <x < 3, 0 otherwise. fy (y) = Y(5 – y)³, 0 < y< 5, 0 otherwise. a. Are X and Y independent? O yes O no O not enough information to determine 提交答案| Tries 0/10 Find Cov(X,Y). Give your answer to 4 decimal places. 提交答案 Tries 0/5 b. Suppose we know that Alex purchased 2 pounds of Skittles. What is the probability that he bought less than 1 pound of M&M's? That is, find P(X < 1| Y=2). Give your answer to 4 decimal places. 提交答案| Tries 0/5 c. Suppose we know that Alex purchased more than 2 pounds of Skittles. What is the probability that he bought less than 1 pound of M&M's? That is, find P(X < 1 | Y > 2). Give your answer to 4 decimal places. 提交答案 Tries 0/5 d. Find E(X|Y=y). Enter a formula in the first box and two numbers in the second and third boxes corresponding the range of y. Use * for multiplication, / for division and ^ for power. For example, 12/15*y^2*(3-y)^3 means 12 y2(3-y)/15. E(X|Y=y) = < y < O otherwise. 提交答案 Tries 0/15 e. Suppose we know that Alex purchased 1 pound of M&M's. What is the probability that he bought more than 2 pounds of Skittles? That is, find P(Y > 2 | X=1). Give your answer to 2 decimal places. 提交答案| Tries 0/5 f. Suppose we know that Alex purchased 2 pounds of M&M's. What is the probability that he bought less than 1 pound of Skittles? That is, find P(Y < 1 | X=2). Give your answer to 2 decimal places. 提交答案 Tries 0/5 g. Find E(Y|X=x). Enter a formula in the first box and two numbers in the second and third boxes corresponding the range of x.
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