1- Given a single observation x(0) from a uniform distribution [0,1/0], it is desired to estimated 0. It is assumed that > 0. Show that for an estimator = g(x(0)) to be unbiased we must have: So g(u)du = 1
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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.If X is a Poisson variate with mean 2, show that E(x³)= AE(X +1). If 2 =1 show that E\X –1| =2 e CS Scanned with CamScanner8. 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)
- t x, x, ... x be a random sample from an exponential distribution with parameter 0. Find sufficient estimator for '8'.Show that the mean x of a sample of size n from the distribution. e-x/0 f (x)=- A i 06. Find the mean and variance of fx (x) = 2e eA* la.2...) (x) = deIn this question you are required to examine distribution at X(0) and x(1/8fo) x(0) ∈{0,-1 ,1} X(1/8fo)∈{1/(√2), -1/(√2)} Show that is not strict sense stationarySEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage