A company sells boxes of savory items X and Y. The weight of each box is 1/2 kg, but the individual weights of the savory item X and savory item Y vary from box to box. For a randomly selected box, let X and Y have the joint density function f(x, y) ={ 24xy 0<=x<=1/2, 0<=y<=1/2, x+y<=1/2 { 0 elsewhere. (a) Find the marginal density for the weight of the Y savory item. (b) Find the probability that the weight of the Y savory item in a box is less than 1/8 of a 1/2kg if it is known that X savory item constitute 3/4 of the weight.

A company sells boxes of savory items X and Y. The weight of each box is 1/2 kg, but the individual weights of the savory item X and savory item Y vary from box to box. For a randomly selected box, let X and Y have the joint density function f(x, y) ={ 24xy 0<=x<=1/2, 0<=y<=1/2, x+y<=1/2 { 0 elsewhere. (a) Find the marginal density for the weight of the Y savory item. (b) Find the probability that the weight of the Y savory item in a box is less than 1/8 of a 1/2kg if it is known that X savory item constitute 3/4 of the weight.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A company sells boxes of savory items X and Y. The weight of each box is 1/2 kg, but the

individual weights of the savory item X and savory item Y

vary from box to box. For a randomly selected box, let X and Y have the joint density

function

f(x, y) ={ 24xy 0<=x<=1/2, 0<=y<=1/2, x+y<=1/2

{ 0 elsewhere.

(a) Find the marginal density for the weight of the Y savory item.

(b) Find the probability that the weight of the Y savory item in a box is less than 1/8 of a

1/2kg if it is known that X savory item constitute 3/4 of the weight.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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