Errors in an experimental transmission channel are found when the transmission is checked by a certifier that detects missing pulses. Let XX be the number of errors found in an eight- bit byte with the following PMF. 1 4 7 p(x) 0.7 0.2 0.1 Determine the mean of X, E(X:), Var(X), and Compute E(X:)-[E(X)]?.
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- Which one is correct? Consider the Cobb- Douglas production function, Q = aK^bL^c ; b and ca) Can be estimated using OLS on the equation Q = a +bK+cL b) Can be calculated from the covariances of K and L with Qc) cannot be estimated using OLS d) can be estimated using OLS on the equation log(Q) =log(a) +b log(K) +b log(L)A hypothesis test produces a t statistic of t=2.01.If the researcher is using a two tailed test with x=0.05,how large does the sample have to be in order to reject the null hypothesis?Let X1, . . . , Xn, . . . ∼ iid Bern(θ). Consider the Bayes estimator under squared error loss with the Unif(0,1) prior. Show that this estimator is consistent.
- Let X ,X , ,X 1 2 n … be a random sample of size nfrom a population with mean μ and variance σ2.(a) Show that X2 is a biased estimator for μ2.(b) Find the amount of bias in this estimator.(c) What happens to the bias as the sample size n increases?A veterinary nutritionist developed a diet for overweight dogs. The total volume of food consumed remains the same, but one-half of the dog food is replaced with a low-calorie “filler” such as canned green beans. Six overweight dogs were randomly selected from her practice and were put on this program. Their initial weights were recorded, and they were weighed again after 4 weeks. The results of the experiment are shown below. At α=0.05, can it be concluded that the dogs significantly lost weight?A population of trees has a mean leaf length of 6.2 inches. A sample of 17 of these trees in a particular neighborhood has a mean length of 3.2 inches. If SS = 144 for this sample, what is Cohen's d for this example, and what is the strength of the treatment effect, which in this case is growing in a particular neighborhood?
- To increase egg production, a farmer decided to increase the number of times the lights in his henhouse were on. Ten hens were randomly selected, and the number of eggs each produced was recorded. After one week of lengthened light time, the same hens were monitored again. The data is given here. At α = 0.05, can it be concluded that the increased light time increased egg production? Hen 1 2 3 4 5 6 7 8 9 10 Before 4 3 8 7 6 4 9 7 6 5 After 6 5 9 7 4 5 10 6 9 6A manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Determine the following. 1) E(x)2) E(Y|X=2)3) V(Y|X=2)4) Are X and Y independent? Why?(Yi, X1i, X2i) satisfy the assumptions of the attachment in addition,var(ui | X1i, X2i) = 4 and var(X1i) = 6. A random sample of size n = 400is drawn from the population.a. Assume that X1and X2 are uncorrelated. Compute the variance of β˄1.b. Assume that corr(X1, X2) = 0.5. Compute the variance of β˄1. c. Comment on the following statements: “When X1 and X2 are correlated,the variance of β˄1 is larger than it would be if X1 and X2 were uncorrelated. Thus, if you are interested in β1, it is best to leave X2 out of the regression if it is correlated with X1.”
- we are given independent random variables X and Y distrubuted: X ∼ poisson(θ) , Y ∼ poisson(2θ), and observations x = 3 and y = 5. Show that the expression for the log-likehood function is given by: l(θ)=[5ln(2)−ln(3!)−ln(5!)]+8lnθ−3θ. make a sketch of l(θ) for θ ∈ [0, 10]. for which value of θ does l(θ) reach its maximum?-Suppose we fail to reject Ho: μ ≥ 50 When the true mean is μ = 53Given a sample of size n=64 and σ =6 and with α=0.05Calculate the critical sample mean Xα , the ZX̅α , The probability of type II error βand the power of the hypothesis test P.Solution: [Write the rules/formula]Calculate X̅α :Calculate ZX̅α with the true mean μ = 53:The probability of type II error β:The power of the hypothesis test P:A sample of n = 64 scores has a mean of M = 68. Assuming that the population mean is μ = 60, find the z-score for this sample: If it was obtained from a population with σ = 16 z = If it was obtained from a population with σ = 32 z = If it was obtained from a population with σ = 48