Generate a matrix containing 5000 samples from the Weibull distribution with a = 1 and B = 2, each of size n = 100. Compute the 500 means using the apply function and store it in x2matmn. Call this variable X2.
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- Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?... Which of the estimators have a variance of 7 X1+X2++X, 7 2X1-X6+X4 2 3X1-X3+X4 2 2(X1+X2+.+X¬) 4 7Check whether the data in this problem satisfy the Hawkins–Simoncondition.a production line is producing light bulbs. 90% of the bulbs are good and .10% are defective. Suppose each bulbls condition is dependent of the other bulbs condition Select three buls at randon: 1. P(all 3 are good)=? 2. P( 2 of 3 are good)= 3. P(1 of 3 are good)=
- Let X,, X2, and X3 be independent random variables, each are binomially distributed with n = 100 and p = 0.2. Let A = X,– 2X2 and B = X3 + 3X1. Find PAB- %3D %3DLet U1 and U2 be two iid U(0,1) random variables. Show that U1 and 1 - U2 have the same distribution by showing their CDFs are the same3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
- The built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convert this column into the vector x by the assignment x30 we can create a confidence interval for μ using a normal critical value. If we want the confidence interval to be at the 94% level and we use a normal critical value, then what critical value should we use? i) Calculate a 94% confidence interval(using a normal critical value) for μ.Define β1 stands for?A selected, inbred rat strain had a tail measuring an average of 5.4 cm. An inbred, wild caught strain had 6.2 cm long tails. The selected and wild caught strains were crossed producing the F1 and F2 below. Generation Progeny Phenotype F1 20 5.8 cm F2 250 5 to 6.6 cm a) Assume that 4 genes control tail length. What is the average contribution per allele in the F2 generation? b) What proportion of the F2 would have tails 6 cm in length? c) Which of the following best describes the PARENTAL rat strains? AAbbCCDD x aaBBccdd AABBCCDD x aabbccdd AABBccdd x aabbCCDD d) How many offspring (approximately) in the F2 would have 5 cm long tails?
- Suppose we take a random sample of size 25 form Bi(10, p). Find the pmf and the CDF of the 5th order statistic Y3.Consider an MA(2) model: STEPS -Write the equation of the M(2) model-Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.