4.3-3. Let W equal the weight of laundry soap in a 1-kilogram box that is distributed in Southeast Asia. Suppose that P(W< 1) = 0.02 and P(W> 1.072) = 0.08. Call a box of soap light, good, or heavy, depending on whether (W< 1), 11 ≤ W≤ 1.072), or (W> 1.072), respectively. In n = 50 independent observations of these boxes, let X equal the number of light boxes and Y the number of good boxes. (a) What is the joint pmf of X and Y? (b) Give the name of the distribution of Y along with the values of the parameters of this distribution. (c) Given that X = 3, how is Y distributed conditionally? (d) Determine E(Y|X = 3). (e) Find p, the correlation coefficient of X and Y.

4.3-3. Let W equal the weight of laundry soap in a 1-kilogram box that is distributed in Southeast Asia. Suppose that P(W< 1) = 0.02 and P(W> 1.072) = 0.08. Call a box of soap light, good, or heavy, depending on whether (W< 1), 11 ≤ W≤ 1.072), or (W> 1.072), respectively. In n = 50 independent observations of these boxes, let X equal the number of light boxes and Y the number of good boxes. (a) What is the joint pmf of X and Y? (b) Give the name of the distribution of Y along with the values of the parameters of this distribution. (c) Given that X = 3, how is Y distributed conditionally? (d) Determine E(Y|X = 3). (e) Find p, the correlation coefficient of X and Y.

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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