Inclass we covered the derivation of basic learning algorithms to derive a model for a coin flip  Consider a similar problems where we monitor the time of the occurrence of a severe computer failure (which requires a system reboot) and which occurs according to a Poisson process (i.e. it is equally likely to happen at any point in time with an arrival rate of λ ). For a Poisson process the probability of the first event to occur at time x after a restart is described by an exponential distribution:ml作业代写−pλ(x) = λe ml作业代写 项目介绍We are assuming here that the different data points we measured are independent, i.e. nothing changes between reboots.Derivethe performance function and the optimization result for analytic MLE optimization for a model learning algorithm that returns the MLE for the parameter λ of the model given a data set D = {k1, kn}. Make sure you show yourApply the learning algorithm from a) to the followingdataset:D = {1.5, 3, 2.5, 2.75, 2.9, 3} .  Derive the optimization for a MAP approach using the conjugate prior, the GammaThe Gamma distribution is:pα,β(λ) =βα Γ(α)λα−1−βλml作业代写 Note that α and β are constants and that there still is only one parameter, λ, to be learned. Show your derivation and the result for the data in part b) and values for α and β of 5 and 10, respectively.K Nearest NeighborConsider the problem where we want to predict the gender of a person from a set of input parameters, namely height, weight, and age. Assume our training data is given asfollows:

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