X1,...,Xp~EXP(0) Ho:0 = 0, VS Ha : 0 # 0, Determine GLRT size a (Note: use the sample approach big)
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Q: A one-sample zz-test for a population proportion pp will be conducted. Which of the following…
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Q: 3. In a test of Ho: µ = 85 against Ha: µ> 85, the sample data yield the sample statistic z = 1.64.…
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- Find the average value over the given interval. y=7e^-x; [0,5]The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanationAssume the pressure capacity of foundation is normal variate, Rf ~N(60, 20) psf. The peak wind pressure Pw on the building during a wind storm is given by Pw = 1.165×10-3 CV2 , in psf where C is the drag coefficient ~N(1.8, 0.5) and V is the maximum wind speed, a Type I extreme variate with a modal speed of 100, and COV of 30%; the equivalent extremal parameters are α=0.037 and u=100. Suppose the probability of failure of the given engineering system due to inherent variability is Pf=P(Rf - Pw ≤ 0). Obtain the Pf using Monte Carlo Simulation (MCS) with the sample size of n=100, 1000, 10000, and 100000. Show the estimated COVs for each simulation.
- Let X be a standard normal RV. Suppose Y = 2X+3 and Z = -X+6. a) Find the covariance between Y and Z b) Find the correlation coefficient between Y and ZConsider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)What portion of the area under the normal curve can be found between z=0 and z=2? What portion of the area under the normal curve can be found to the left of z= - 1.25?
- Find the area and normal curve Less than z = -2.11Let X1,...Xn be iid Normal(θ + c, σ^2), where c and σ^2 are known constants (i.e., E(Xi) = θ + c). Find a sufficient statistic for θ. Use this sufficient statistic to obtain an MVUE for θ.Experience has shown that the weight of lemons produced by an orchard isnormally distributed, with an average weight (µ) of 100g and a standarddeviation (σ) of 8g. A sample of 150 of these oranges is randomly selected. Determine the margin of error for 99% ci for sample mean
- The joint PDF of the random variables X and Y is constant on the region (x,y):x≥0∩yleq1∩−0.5≤x−y≤0, shown in the image below, and is zero outside. Determine P(Y>0.5|X<0.5)Determine the kurtosis if the data given is a sample. Use 4 decimal placesLet X be a random variable with exponential distribution having lambda=6 and let Y = 3X. a. Find P(X>0.25) b. Find the mgf of Y c. Find the pdf of Y