16) A stationary random process has an autocorrelation function of -Siz Ry(t)=16-e cos 20rt+8 cos10TT. Find the variance of this process.
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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 PSD of a stationary random process for which Auto correlation is Rx (t)= 6- e altiDerive that the variance of the forecasted error using Exponential Smoothing (ES) method is given by 20² Var(et) 2 – α Where o² is the variance of individual observation and a is the parameter in the ES method. =
- If a random variable X has the moment generating function Mx (t)= 2 - ť Determine the variance of X.Suppose you fit a simple Poisson model such that in A = XB where B = 1.9. What would the variance be if x = -0.8 ?2.2 Explain how to generate from the Beta (1, 3) distribution using the inverse- transform method.
- let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x isShow that the mean of a random sample of size n from an exponential population is a minimum variance unbi-ased estimator of the parameter θ.Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is p(1-p)