A normally distributed streamflow random variable has mean and a standard deviation respectively of 4 m3/s and 2 m3/s.
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10 and its return period (also know as recurrence interval).
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- Which of the following is true of fixed effect estimators A. The fixed effects estimator is equal to the instrumental variable estimator if R^2 is equal to 1. B. The fixed effects estimators are biased if the regression model exhibits multicollinearity. C. The fixed effects estimators have lower variance than the ordinary least squares estimators. D. The fixed effects estimators have large standard errors when R^2 lies close to 0.Suppose model (XY, XZ, YZ) holds in a 2 x 2 x 2 table, and the common XY conditional log odds ratio at the two levels of Z is positive If the XY and YZ conditional log odds ratios are both positive or both negative, show that the XY marginal odds ratio is larger than the XY conditional odds ratio.Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin, - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team===== "Brooklyn Nets" . Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1459.95122 1 80 190.65061 None of the above 81 206.320988 Coef. Std. Err. 8.439024 3.049595 -5.219512 2.156389 MS t Number of obs F(1, 80) Prob > F R-squared O The Nets lost more games than they won in 2014 P>|t| 2.77 0.007 -2.42 0.018 Adj R-squared = Root…
- Let Z be a st andard normal variable. Let mean and standard derviation > 0 be two real numbers. Then, the distribution of the random variableIs X=emean+standard derviation*Z called the Lognorma (mean,standard derviation) distribution. Write a function to generate random variables from this Lognormal distribution using a transformation method and generate a random sample of size n = 1000. Compare the histogram with the lognormal density curve given by dlnorm function in R.The time to failure (in hours) of a piece of equipment is uniformly distributed over (0, 1000) hours. (a) Determine the MTTF. (b) Determine the MTTF if preventive maintenance will restore the system to as good as new condition and is performed every 100 operating hours. (c) Compare the reliability with and without preventive maintenance at 225 operating hours. Assume the 100 hour maintenance interval and a maintenance-induced failure probability of 0.01 each time preventive maintenance is performed.Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
- A manufacturing process produces semiconductor chips with a known failure rate of 7.5%. If a random sample of 265 chips is selected, approximate the probability that more than 16 will be defective. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.Heteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: Var(et)=σt^2=σ^2 xt. But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: (Picture 1) Where var(et)=σ^2 according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do a different correction to get rid of it. (a) what correction would you use…A disk drive has a constant failure rate and an MTTF of 5000 hr. (a) What will the probability of failure be for one year of operation? (b) What will the probability of failure be for one year of operation if two of the drives are placed in active parallel and the failures are independent? (d) What will the probability of failure be for one year of operation if the system si changed to standby model. (e) Describe the effect on the MTTF with a switching failure probability of 0.05. () What would be change in MTTF if the probability of failure of standby unit is 10 percent of the failure of the primary unit in the standby mode?
- Suppose that X₁ = 1; X₂ = 1; X3 = 0; X₁ = 1; X5 = 1, X6 = 1; X₂ = 0; X = 1; X9 = 0, X10 = 0, represents a random sample. Each of these X's comes from the same population and has a density of fx₁ = 0¹-* (1 - 0)*; x = 0,1 First determine the form of the maximum likelihood estimator for 0, then use the MLE formula and the data provided to find an estimate for 0. Round your answer to 3 decimal places. (Answer is 0.4)Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)An machine with constant failure rate 0.002 per hours is operated 8 hours per day, 230 days per year. The mean downtime required to repair the machine and bring it back into operation is MDT = 5 hours. The machine can only fail during active operation. If a repair action cannot be completed within normal working hours, overtime will be used to complete the repair such that the machine is available next morning. (a) Determine the average availability of the machine (during the planned working hours). (b) Determine the average availability of the machine if the use of overtime were not allowed.