Pfoblem 8. Given x = Px, + w, where 'm is white but not gaussian. What is the mean and covariance equation for x, ?
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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.The variation of Y around its mean can be decomposed into which two parts?It T is an unbiased estimator for 0, show that T² is a biased estimator for &.
- 3. a. B (0.25, 0.75) Evaluate using Beta Function:The value of the correlation r = (x,y) for the information would be: n = 8, Sum(x) = 609, Sum(y) = 504, Sum (x)^2 = 47995, Sum (y)^2 = 32954, and Sum (xy) = 395650 Choose answer from the following: a. 0.855 b.0.174Q/ Consider the following four points to interpolate for y = f(3.2) using: 1.0 0.1111 2.0 0.0625 3.0 0.0400 4.0 0.0278 1. Direct Fit Substitution.
- Q5. The correlation coefficient will be zero when A. ΣΧ-X) (Υ - )= 0 B. E(X – X)² = 0 C. [(Y – Ỹ)² = o | | | D. Not possible to tell without knowing all the values. O A. A В. В O C. C O D. DQ/The following data shows the relationship between x and y. Use interpolation technique to find the value corresponding to (x = 4). (x: 2, 3, 5, 8, 12), (y: 10, 15, 25, 40, 60) *EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.
- If I let X1, X2, . . . , Xn ∼i.i.d Exp(λ) with n > 1. how do I find unbiased estimators for this and computer the mean squared error? which estimattor is betterThe correlation between X and Y Select one or more: a. is the covariance squared b. cannot be negative since variances are always positive. c. is given by corr(X, Y) = cov(X,Y)/var(X)var(Y)cov(X,Y)/var(X)var(Y) d. can be calculated by dividing the covariance between X and Y by the product of the two standard deviationsSuppose that X1, X2,... Xn are n values of a variable X and X is the arithmetic mean. Can we obtain a measure of dispersion of X by taking the arithmetic mean of the deviations (X; - X)? If not, suggest how we can use these deviations to obtain a measure of dispersion of X.