A random sample of size n is taken from an exponential population and is used to test Ho: 0=00 H₁:000 1 Using the pdf forme-2/0 (a) find the Likelihood Ratio Test statistic and (b) show that the critical region can be written as for some number K. X-exp(-x) ≤ SK
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- two random independant variables X and Y with distributions: X ∼ Poisson(λ) og Y ∼ Poisson(2λ), andobservations x = 2 og y = 5 .(a) What is the log-likelihood function? b) calculate MLE for the observated samplesLet the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.The useful life of a concrete built on the seashore has a Weibull distribution of parameter scale δ> 0 year and power β = 2. Determine a) The half life of concrete EXb) The variance VXc) The probability that the concrete lasts more than 10 years; P (X> 10)
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