As soon as possible！Write by hand （step by step） =# 2. Let X be a Laplacian random variable with PDF fx(x) =a > 0. Consider Y = X², and find its PDF, fy(y).e-ax,# 3. Let X be an exponential random variable with PDF fx(x) = ae¯αxu(x),a> 0. Consider Y = ex and find its PDF, fy(y).

Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Answered: = e-α|x|, #2. Let X be a Laplacian…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 31E

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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.
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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
Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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= e-α|x|, #2. Let X be a Laplacian random variable with PDF fx(x) a> 0. Consider Y = X2, and find its PDF, fy(y). # 3. Let X be an exponential random variable with PDF fx(x) = ae-α* u(x), a> 0. Consider Y = = ex and find its PDF, fy(y).