Solution Found!
Let W equal the weight of laundry soap in a 1-kilogram box that is distributed in
Chapter 4, Problem 4.3-3(choose chapter or problem)
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}, {1 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 , the correlation coefficient of X and Y.
Questions & Answers
QUESTION:
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}, {1 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 , the correlation coefficient of X and Y.
ANSWER:Step 1 of 6
Given that,
The W equals the weight of laundry soap in a 1-kilogram box that is distributed in Southeast Asia.
The number of independent observations of the boxes=50.
and
The X equals the number of light boxes and Y the number of good boxes.