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.

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…

How many of these components (each having a failure rate of 0.005 failures per hour) must be placed in parallel if the system is to run for 10 hours with a system failure probability of more than 0.0005? Assume that all failures are independent. 07

2. An experiment was conducted to explore the effects of fatigue on the performance of a simple manual task. A random sample of 15 male, college students was obtained. We will assume that this sample forms a random sample from all of the male, college students that were available to the investigators. These students were trained to make a continuous horizontal right-to-left arm movement from a microswitch to a barrier, so that the barrier was knocked over at exactly the same time as the clock sweep second hand arrived at the 6 o'clock position. The absolute value of the difference between the time, in milliseconds, that it took to knock over the barrier and the time for the sweep second hand to reach the 6 o'clock position was recorded. Note that the student's goal is to make this time difference as close to zero as possible. Each participant performed the task five times under rested conditions (the student was not fatigued) and fatigued conditions (the student was fatigued). The sums…

Suppose Y₁,..., Yn are independent random variables each with the Pareto distribution and E(Y) = (Bo + B1Xi) Is this a generalized linear model with a canonical link? Give reasons for your answer.

I JIO 4G 10:03 VOLTE You ぐ Just now 8. A market investigator returns the following' data. Of 1,000 people consulted 811 liked chocolates, 752-liked toffees and 418 liked boiled sweets, 570 liked both chocolates and toffees, 356 liked chocolates and boiled sweets and 348 liked toffees and boiled sweets, 297 liked all' three. Show that this information as it stands must be incorrect.

As soon as one components fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with ? = 0.01 and that components fail independently of one another. Define events Ai = {ith component lasts at least t hours}, i = 1, . . . , 5, so that the Ais are independent events. Let X = the time at which the system fails—that is, the shortest (minimum) lifetime among the five components. P(X ≥ t)?  F(t) = P(X ≤ t)? the pdf of X?

The process for cleaning up waste in a nuclear reactor core room eliminates 85% of the waste present in the area. If there is 1.7 kg of waste in the room at the beginning of the monitoring period and 2 kg of additionalwaste are generated each week, determine a recurrence relation and initial conditions describing the amount wn, of waste in the core room at the end of week n of the monitoring period.

An alloy manufacturer is investigating if they can improve the strength of one of their alloysby producing it at a lower temperature. To investigate that, they produce the alloy at twodifferent temperatures (high and low) and then measure the breaking strength of randomsamples of specimens from each. The following table represents the strength of the randomsamples at the higher and lower temperature, in units of 0.001-inch deflection.  Temp. Strength (0.001 inch)High 87 64 66 85 76 49 97 73 75 77 69 68 89 27 58 84Low 88 82 81 85 79 80 88 78 77 85 79 76 Do the results support the hypothesis that lowering the production temperature can improve thestrength of the alloy, with 95% confidence? (Hint: Don’t forget investigating variances. Use 98% confidence for that.)

18. In a bank there are 2 checkouts, each with its own row of infinite size: checkout 1 for “fast” customers, with a time of 2 minutes, and checkout 2 for “slow” customers, with a time of 16.4 minutes, in both cases with exponential distribution. “Slow” and “fast” customers arrive according to an exponential function, with mean 8 and 20 minutes/customer, respectively. Some days, in particular, only 1 cashier comes to work who has to serve both lines according to the following cyclical sequence; 5 “fast” clients and 2 “slow” clients. The time to move between the boxes is 0.33 minutes. Simulate the process in ProModel for 80 hours and determine:   The average number of customers waiting in each queue.   The optimal service sequence to minimize waiting time, considering both types of customers.