Question 7Suppose the distribution of Y, conditional on X,is n(x, x²) and that the marginal distribution ofX is uniform(0, 1).(a) Find EY, Var Y, and Cov (X, Y). (b) Prove thatY/X and X are independent.

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Answered: Suppose the distribution of Y,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 24E

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Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
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Suppose the distribution of Y, conditional on X, is n(x, x²) and that the marginal distribution of X is uniform(0, 1). (a) Find EY, Var Y, and Cov (X, Y). (b) Prove that Y/X and X are independent.