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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?
- A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?If X has an exponential distribution, show thatP[(X Ú t + T)|(x ÚT)] = P(X Ú t)A random variable X has the pdf as f(x) = ax + b, for 0(1) Let X = b(16,- find E(4-3x) and distribution function.gn X Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.41 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) P(X = X) X 0 1 2 3 4 5 6 7 8 (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) X 0 1 2 3 4 5 6 7 Use the cumulative distribution function of X to calculate P(2 ≤ x ≤ 5). (Round your answer to four decimal places.) P(2 ≤ x ≤ 5) = Need Help? Read It Watch It 4The lung cancer hazard rate λ(t) of a t-year-old male smoker is such that λ(t) = 0.027 + 0.00025(t-40)2, and t >= 40. Assuming that a 40-year-old male smoker survives all other hazards, (a) what is the probability that he survives to age 50 without contracting lung cancer?(b) what is the probability that he survives to age 60 without contracting lung cancer?A random process X(t) is applied as input to a system whose impulse response is h(t) 3u(t)t² exp (-8t). If E[X(t)] = 2, what is the mean value of the system response y(t). - CS Scanned with CamScannerIf E[X] = 1 and Var(X) = 5, use definition of variance and properties of expectation to find (a) E[(2 + X)^2] (b) V ar(aX) for any constant a. (c) V ar(X + b) for any constant b. (d) V ar(4 + 3X)The time t (in hours) required for a new employee to succesfully learn to operate a machine in a manufacturing process is described by the probability function f(t) = kt/16 – t for 0SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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