Please answer parts 1, 2, and 3 of the question below. Show all work and steps. Suppose X -Exp(B) with density fx(x) = Bexp(-Bx) for x > 0and B > 0. For Y = X/, where y > 0 is a constant, derive the following1.The PDF of Y, fy(g). Show that it integrates to 1.2.The expectation, E[Y].3.The variance, V[Y].

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Answered: Suppose X - Exp(B) with density fx(x) =…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 2E

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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.
The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
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Suppose X - Exp(B) with density fx(x) = Bexp(-Bx) for x > 0 and B > 0. For Y = X/, where y> 0 is a constant, derive the following 1. The PDF of Y, fy(g). Show that it integrates to 1. 2. The expectation, E[Y]. 3. The variance, V[Y].