Appreciate the help!! Problem 6. Suppose (X₁, X₂) have joint density[6x₁x² 0

a) To find the joint density of (Y1, Y2), we need to use the transformation method. Let g(Y1, Y2) be…

Answered: Problem 6. Suppose (X₁, X₂) have joint…

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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A pharmaceutical company wanted to study the effectiveness of a new hair growth product in women. It recruited 1100 random women from the L.A. area and measured the length of their hair. They gave 500 women the new product in unmarked bottles to use over a 6-month period. The other 600 women received unmarked bottles with mostly water and fragrance to use over a 6-month period. None of the women knew which product they received. They found that 450 out of 500 women that received the new product showed hair growth of 1-2 inches. Only 90 out of 600 women that used the water/fragrance combination showed hair growth of 1-2 inches. Women who received the treatment are Blank %/ blank % = Blank times to show hair growth.
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You Got Gas have developed a new type of fuel additive that supposedly increases car speed. Before they put it out on the market, however, they need to test if it really is a difference compared to standard fuel. So, they took 6 vehicles and calculated the time it takes to for them to drive 1 mile going as fast as they can. They received the following data: Car ID# Course time (standard fuel in minutes) Course time (w/ additive in minutes) 1 35 27 2 40 35 3 25 27 4 40 39 5 95 94 6 32 18 6. What is the null and research hypothesis for this study? 7. What type of statistical test should we use to compare means (z-test, independent t-test, dependent t-test, or ANOVA)? Why? 8. What are the degrees of freedom? What are the critical values for that statistical test with this data at α = 0.05? α = 0.01? 9. Comparing the groups, is there a significant difference at α = 0.05 in lap time between eating the name bran and when they ate Dog Go? 10. How would the researcher…

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Problem 6. Suppose (X₁, X₂) have joint density (1₁,1₂)= [6x₁1² 0