(c) What is the asymptotic distribution of √n(0-0)?6.2.9. If X1, X2,..., Xn is a random sample from a distribution with pdf={f(x; 0) =303(x+0)400

Answered: Image /qna-images/answer/d78cf4a3-3fea-4555-b39f-538a40077138.jpg

Answered: 6.2.9. If X₁, X2,..., Xn is a random…

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.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 26E

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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.
Repeat Example 1a for the function f(x)=2x2 on [1,2]. What is the probability that X will be between 32 and 2?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
The CDF F(x) of a random variable X is given by; F(x) = { 0, ?? ? ≤ 1 ?(? − 1)^4 , ?? 1 < ? ≤ 3 1, ?? ? > 3 } (i)find PDF f(x) (ii) ?(|?| < 1.5), (iii) the mean and variance of X.

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6.2.9. If X₁, X2,..., Xn is a random sample from a distribution with pdf 303 f(x; 0) (x+0)4 = -{ 0