5.2.20. Find the method of moments estimate for λ if a random sample of size n is taken from the exponential pdf, fy(y; ) = hey, y ≥ 0.
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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.Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.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
- 6. (Sec. 5.1) Two headlights of a car have the following joint pdf for their useful lifetimes X (the left headlight) and Y (the right headlight) ze(y+1) for r> 0.y > 0 f(x, y) 0 otherwise (a) What is the probability that the lifetime X of the left headlight exceeds 2.8? (b) Find the marginal pdfs of X and Y. Are the two lifetimes independent? Justify your answer (c) What is the probability that the lifetime of at least one headlight does not exceed 2.8?2.5.8) Suppose that Y is a continuous random variable whose pdf is given by f(y) = {K (4y = 2y²), 0 1). (c) Find F(y).9. Let Y1, Y2,..., Yn constitute a random sample from the pdf given by f (y) = 2 (0 – y) for 0 < y <0. %3D Find an estimator for 0 by using the method of moments. estimator =