5. Suppose we have three types of GPU's: A, B, C - at a super-computing facility. The time taken by each of the GPU: A, B, C - to perform a given task is model by exponential distributions Exp(A4), Exp(λB = 1), Exp(Ac = 0.2) respectively. Additionally, there are a total 10 GPUs, 2 of which are of Type A, 5 are of Type B, and the remaining are of Type C. When a task arrrives at the facility, we randomly assing the task to one of the 10 GPUs. (a) What is the probability that a task arriving at the computing center will be finished in 2 hrs? (b) What is the probability that a task arriving at the center will take between 1 and 4 hours? (c) What is the expected amount of time to finish a task arriving at the center? Show the setup and all work.

Consider a two component parallel system in which both components have times to failure and times to 0.0024 f/hr and µ1 = = 0.001 f /hr, 12 repair that are exponentially distributed. The data is 1, 0.003 r/hr and µ2 = 0.005 r/hr. Evaluate the reliability or probability of success for a mission of 1000 hr. (hint: form a history for each component using the data for failure rate and repair rate)

Consider a model with an interaction term between being female and being married. The dependent variable is the log of the hourly wage: log(wage) = 0.151 - 0.038 female + 0.1 married - 0.301 female* married + 0.079 educ + 0.027 exper+0.029 tenure (0.072) (0.056) (0.055) (0.007) (0.005) (0.007) n = 536, R2 = 0.461 Numbers in parantheses are standard errors of coefficients. Given the estimation result and the observation number fill in the blanks below which aim at discussing the statistical significance of variables. The test statistic of the interaction term is The critical value at 1% significance level is Then the interaction term statistically significant at 1% significance level. (Hint: to fill the blank make a choice between "is" and "is not".)

In various places in this module, data on the silver content of coins minted in the reign of the twelfth-century Byzantine king Manuel I Comnenus have been considered. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and fourth coinage (variable Coin4) which was produced a number of years later. it was argued that the silver contents in both the first and the fourth coinages can be assumed to be normally distributed. The question of interest is whether there were differences in the silver content of coins minted early and late in Manuel's reign. You are about to investigate this question using a two- sample t-interval. COINS (21.MWX Two-Sample T-Test and CI: Coin1, Coin4 A COINS (2)MWX Two-Sample T-Test and Cl: Coin4, Coin1 Method Method mean of Coin1 Pa mean of Coind Difference u- 4 mean of Coin4 z mean of Coint Difference: - Vz Equal variances ore assumed for this analysis Equal variances ore assumed for this…