please solve all parts Example: Let X be a continuous random variable with PDFFile Preview8'f(x) = { 3 0 2 0 ≤ x ≤ 2(a) Sketch a graph of the PDF f(x).0 otherwise.Poll Question 7.6(b) Find E(X).(c) Find E(X2).(d) Find V(X).

Answered: Image /qna-images/answer/dcc7bff2-a23e-4689-a7ea-9c79acd45210.jpg

Answered: (b) Find E(X). (c) Find E(X2). (d) Find…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 1E

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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.

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(b) Find E(X). (c) Find E(X2). (d) Find V(X).