C# Visual Studios, Windows Forms App .NET framework GHG projectI am struggling in visual studios to get my DGV to show and to get it to run once it does show.I have a good bit of part one completed and the feedback i have is : validations are not set up correctly and I cannot bypass past first name. Please see documentation in D2L under slides and videos to fix. Donation file: submit button does not feed to DGVDonor FILE: -Donor type has incorrect drop down information-DGV does not have pre-populated data. Please see slides from last class with instructions on how to do this.I need the part 2 completed on both Donor and Donation,all instructions are attached as well as the code i had started for each donor and donation
Homework 3: Continuous Variables & ClassificationUC Irvine CS177: Applications of Probability in Computer ScienceDue on November 10, 2020 at 11:59pmQuestion 1: (20 points)The time that a TA spends helping an individual student in office hours is exponentiallydistributed with a mean of 8 minutes, and independent of the time spent with other students.For an exponential distribution with parameter θ,fX(x) = θe−θx for x ≥ 0, E[X] = 1θ, Var[X] = 1θ2.Suppose there is a homework due tomorrow, and there are 4 people ahead of you in line.a) The total time that it takes all 4 students ahead of you to receive help from the TA is arandom variable. What is the mean of this total time?b) What is the standard deviation of the total time taken by the 4 students ahead of you?c) What is the probability that all 4 people ahead of you will each take at most 10 minutes?d) Suppose that the TA has finished helping the first 3 students, and has already spent 10minutes with the fourth student. What is the mean and standard deviation of the amountof additional time you need to wait for help?Question 2: (20 points)An artificial intelligence class has an assignment to write a program that generates the nextmove in a game of chess. Suppose that the runtimes of student programs follow a normaldistribution with mean µ = 13 seconds, and standard deviation σ = 2.0 seconds. Hint: ThePython commands scipy.stats.norm.cdf and scipy.stats.norm.ppf may be useful.a) What is the probability that a random program has a runtime greater than 18 seconds?b) What is the probability that a random program has a runtime between 10 and 16 seconds?c) The TA’s want to help the students complete their work faster. What would they haveto lower the average runtime to so that only 1.0% of students have runtimes over 13seconds? Assume the standard deviation remains fixed at σ = 2.0 seconds.1Question 3: (20 points)You’ve been asked to test the performance of a batch of newly fabricated processors. If theprocessors were correctly manufactured (class Y = 0), the time X to complete your test suiteis exponentially distributed with mean 1. If the equipment at the factory malfunctions (classY = 1), the time X is exponentially distributed with mean 50. You must decide whether ornot this batch of processors was correctly manufactured.For the scenarios in the three parts below, it is possible to show that the optimal Bayesianclassifier predicts Y = 0 if x ≤ c, and predicts Y = 1 if x > c, for some constant c. Thevalue of c depends on the test time distributions, the prior probabilities of the two classes,and the assumed loss function. You need to determine the optimal c in each case.a) Suppose that a new fabrication process has just been deployed, and the probability thatthe factory manufactures correctly functioning processors is only P(Y = 0) = 0.5. Whatthreshold c of the observed test suite time X = x maximizes the probability that yourprediction is correct?b) Suppose that after some improvements to the new fabrication process, the probability thatthe factory manufactures correctly functioning processors increases to P(Y = 0) = 0.99.What threshold c of the observed test suite time X = x maximizes the probability thatyour prediction is correct?c) Market research suggests that the loss (or cost) of a missed detection (predicting Y = 0when the processor is actually defective) is 500 times greater than the loss of a false alarm(predicting Y = 1 when the processor was correctly manufactured). Assuming again thatP(Y = 0) = 0.99, what threshold c of the observed test suite time X = x minimizes theexpected loss?Question 4: (40 points)For a given day i, we let Yi = 1 if the ground-level ozone concentration near some city(Houston, in our data) is at a dangerously high level. This is called an “ozone day”. We letYi = 0 if the ozone concentration is low enough to be considered safe.We want to predict Yifrom more easily measured “features” describing atmosphericpollutant levels and meteorological conditions (temperature, humidity, wind speed, etc.).There are a total of M = 72 of these features collected each day, which we denote byXi = {Xij | j = 1, . . . , M}. Each feature Xij ∈ R is a real number, and we will thus use aGaussian distribution to model these continuous random variables.We will build a “naive Bayes” classifier, which predicts observation i to be an ozone dayif P(Yi = 1 | Xi) > P(Yi = 0 | Xi), and a non-ozone day otherwise. Using Bayes rule, thisclassifier is equivalent to one that chooses Yi = 1 if and only ifpY (1)fX|Y (xi| 1)fX(xi)>pY (0)fX|Y (xi| 0)fX(xi),ln pY (1) + ln fX|Y (xi| 1) > ln pY (0) + ln fX|Y (xi| 0). (1)2In this equation, pY (yi) is the probability mass function that defines the prior probabilityof ozone and non-ozone days. The conditional probability density function fX|Y (xi| yi)describes the distribution of the M = 72 environmental features, which we assume dependson the type of day. We make two simplifying assumptions about these densities: the featuresXij are conditionally independent given Yi, and their distributions are Gaussian. Thus:fX|Y (xi| 1) = YMj=11q2πσ21jexp −(xij − µ1j )22σ21j, (2)fX|Y (xi| 0) = YMj=11q2πσ20jexp −(xij − µ0j )22σ20j. (3)Given Yi = 1, Xij is Gaussian with mean µ1j and variance σ21j. Given Yi = 0, Xij is Gaussianwith mean µ0j and variance σ20j. There are a total of 2M mean parameters and 2M varianceparameters, since every feature Xij has a distinct distribution for each of the two classes.a) Derive equations for ln fX|Y (xi| 1) and ln fX|Y (xi| 0), the (natural) logarithms of theconditional probability density functions in Equations (2,3). For numerical robustness,simplify your answer so that it does not involve the exponential function.Because ozone days are relatively rare, a classifier that always predicts Yi = 0 would becorrect over 95% of the time, but would obviously not be practically useful for reducingozone hazard. To evaluate our classifiers, we will thus separately compute the numbersof false alarms (predictions of ozone days when in reality Yi = 0) and missed detections(predictions of non-ozone days when in reality Yi = 1). We are willing to allow some falsealarms as long as there are very few missed detections.For all parts below, assume that the mean parameters µ1j, µ0j are set to match the meanof the empirical distribution of the training data. The demo code computes these means.b) Start by assuming the classes are equally probable (pY (1) = pY (0) = 1/2), and haveunit variance (σ21j = σ20j = 1). Write code to compute the log conditional densities frompart (a). Then using Equation (1), classify each test example. Report your classificationaccuracy, and the numbers of false alarms and missed detections.Hint: Your classifer should have fewer than 10 missed detections.c) Rather than assuming features have variance one, set the variance parameters σ21j, σ20jequal to the variance of the empirical distribution of the training data. Classify eachtest example using Equation (1) with these variance estimates. Report your classificationaccuracy, and the numbers of false alarms and missed detections.d) Rather than assuming the classes are equally probable, estimate pY (1) as the fraction oftraining examples that are ozone days. Classify each test example using Equation (1) withthis informative class prior, and the variances from part (c). Report your classificationaccuracy, and the numbers of false alarms and missed detections.3
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