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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.bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
- 2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).6. Let X(1) be the minimum value in a sample of n independent observations from the distribution with density f(r) = ae-a(a-#), x > B,a, ß > 0 Find the p.d.f of X(1). Hence find the mean and variance of X(1)-8. Given the Beta Distribution where p(x) = B(a,b).ªªa- Calculate the mean and variance B(a, b) = -xª-¹ (1-x)b-1 1 = √₁² 2²- x-¹(1-x)-¹dx = r(a) I (b) I(a + b)
- 55. Explain from the data given below whether A and B are independent. positively associated or negatively associated : N=10,000, (A) = 4500, (B) = 6000, (AB) = 3150. () (A) = 150, (a) = 250, (B) = 20o, (aB) = 125. %3D %3D %3DA. 58 В. 50 C. 62 D. 48 13. Find the average value of f(x) = v5x on the interval 04. Let Y U (0, 1). Show that X = -2ln(Y) follows an Exponential distribution with mean 2. pplicationsRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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