What is the likelihood ratio p(x|C₁) p(x|C₂) in the case of Gaussian densities?
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- Can you please follow up on the question and answer the second part: 'Propose a transformation of this likelihood function whose maximum is the same and can be computed easily'How do I create a function in python that will calculate the negative log likelihood for a Gaussian model with respect to mean and also variance. Please use data = [10, 25, 10, 8, 8, 9, 10, 22, 12, 13, 15, 4, 8, 9] as the distribution.A confusion matrix based on one particular cut-off probability can determine the entire ROC curve. True False
- Explain how we perform maximum likelihoodGiven 2 patterns at 0.4 and 0.6, estimate probability density analytically using a rectangular window of width 0.3, using a triangular window of width 0.3 and using 1 nearest-neighbour.Prove in the Natural deduction system (∃x, ¬P(x)∧Q(x)) from hypotheses ∃x, ¬P(x) and ∀y, Q(y).
- A random variable X with two-sided exponential distribution given by has moment generating function given by M X (t)= e^ t +e^ -t -2 t^ 2 . f x (x)= x+1,&-1\\ 1-x,&0<= x<=1 - 1 <= x <= 0 (a) Using M_{X}(t) or otherwise, find the mean and variance of X. (b) Use Chebychev inequality to estimate the tail probability, P(X > delta) , for delta > 0 and compare your result with the exact tail probability.Simulate for m=10,100,1000 samples and plot the conditional distribution as given by the analytical expressions of the conditional mean and covariance matrix in Python? ( don't hand writing solution)What must the sum of an HMM probablility distribution be? Why is this the case? Please explain the case properly.
- Specifically, it would be helpful to see an illustration of transition probabilities for a zero-recurrence renewal Markov chain.<s> I am Sam </s><s> Sam I am </s><s> I am Sam </s> <s> I do not like green eggs and Sam </s> If we use linear interpolation smoothing between a maximum-likelihood bigram model and a maximum-likelihood unigram model with lambda1 = 1⁄2 and lambda2=1⁄2, what is P(Sam|am)? Include <s> and </s> in your counts just like any other token.This is an Uncertainty problem. Given the attached table of some probabilities values of a ‘Medical Knowledge-based System’, evaluate ALL posterior probabilities of event, ‘Heart-Attack’ with given hypothesis. Hint: Use Bayesian Theorem