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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.Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator ofIf X ~B(190,0.34), find mean and variance of x. (Rounded in 3dp.)
- Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.Let Y be a random variable with the mgfM(t) = .35e^(−4t) + .1 + .25e^(2t) + .3e^(4t).(a) What is the pmf of Y?(b) Calculate the variance of Y directly from the pmf you determined in part (a).(c) Calculate E[Y^4] directly from the mgf.Suppose a sample Y1, ..., exponential distribution with E (Yi) = 0 and V (Yi) = 02. Let 0^ be an estimator of the mean, 8. Yn is selected from an 1. Explain what a parameter is. What is the parameter of interest in this case? 2. Name the properties of a good estimator and explain, shortly, what is meant by each. (a) (b) (c) 3. Given the properties you discussed in (2) and the parameter of interest identified in (1), what estimator would you propose? 4. What would the sampling distribution of this estimator be? Why?
- X1,., X,Let it be a random sample chosen from a normal distribution with a mean of m and a variance of 10.P (X, – X)² < 44 = 0.025 what is the value of the sample size n? O A. 13 О В. 14 Ос. 11 O D. 12Let X and Y be independent random variables, each with mean=mu and variance=sigma^2. Find the expression of the correlation of X and XY in terms of mu and sigma.Suppose we believe that the life length 'T' (in hours) of light bulb is exponentially distributed with parameter à = 0.005. We obtain a sample of 150 bulbs, test them and record their burning time say T, T2, T3... Ti50 and tabulate Test the hypothesis that the data represent a random sample from an exponential distribution with à = 0.005 at level of significance, a = it 0.01.
- 4 Let f(x) = (1/10)(x-3)^2 for x = 1, 2, 3, 4, 5 %3D Find the standard deviation of X. For the instructor, this was question 11. / 1.8 X 3.1 X 3.4 X 3.5 X 9.4 X 12.4Let's draw chance samples with a width of n1 = 10 from a population showing a normal distribution with a mean of 50 and a variance of 64, and a width of n2 = 9 from a population with a mean of 40 and a variance of 81 showing a normal distribution. If X'1 and X'2 show the sample averages, respectively, then what is the probability P |(X'1 - X'2)> 5| ? (X' = X bar)Suppose that the rate of increase of a bighorn ram's horn is approximated by 0.42 x² - 3.97 x + 31.24 cm per year, where x is between 2 and 5 years. (These numbers have been randomized from the actual equation given in the project done in discussion section.) Find the total change in the length of a bighorn ram's horn between the ages of 2 and 5. Give the answer as a decimal number with at least two decimal places.
