Answered: Check if the measurements of the two…

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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ANSWER LETTER D ONLY

Two measurements method are used to evaluate the surface smoothness of a paper product. Let X and Y denote the measurement of each of the two methods.

a). Suppose that the joint p.d.f. of X and Y is modeled by f_xy(x,y) =c, 0<x<4,0<y and x-1<y<x | 1. Determine the value of c.

b). Determine the marginal probability distribution of X. Find also the mean and variance of X.

c). Determine the conditional probability distribution of Y given X-2. Find also the conditional mean and conditional variance of Y given X=2.

d.) Check if the measurements of the two methods X and Y are independent

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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