2.3.6. Let the joint pdf of X and Y be given byf(x,y) = {(1+x+y)3 0 < x < ∞, 0 < y < xelsewhere.0(a) Compute the marginal pdf of X and the conditional pdf of Y, given X = x.(b) For a fixed X = x, compute E(1+x+Yx) and use the result to computeE(Y|x).

Answered: 2.3.6. Let the joint pdf of X and Y be…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.4: Derivatives Of Exponential Functions

Problem 16E

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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.
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.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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2.3.6. Let the joint pdf of X and Y be given by f(x,y) = { (1+x+y)3 0 < x < ∞, 0 < y < x elsewhere. 0 (a) Compute the marginal pdf of X and the conditional pdf of Y, given X = x. (b) For a fixed X = x, compute E(1+x+Yx) and use the result to compute E(Y|x).