Question 19 If R is a random variable on a sample space S and expected value E(R) = p, then the variance V(R) = E((R-)). O True O False
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- In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where O represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.3 and a standard deviation of 1.9. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected study participant's response was loss than 4. The probability that a randomly selected study participant's response was lons than 4 is (Round to four decimal placos as needed.)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.Given 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.
- PART D The number of false fire alarms in a suburb of Detroit averages 8.4 per day. Assuming that a Poisson distribution is appropriate: What is the probability that exactly 8 false alarms will occur on a given day? What is the probability that less than 8 false alarms will occur on a given day? What is the probability that more than 8 false alarms will occur on a given day? (Hint: the probabilities of all possible cases must add to one).Let X1, X2, .,X25 be i.i.d. random variables from Po(5). Estimate the MSE for the median estimator using Monte Carlo estimation.Write a function my_random that samples a random number from the following discrete probability distribution on the set {8, 9, 13, 15, 17, 18}: P({8}) = ²/ 9 P({9}) = ²/ 18 P({13}) = 1/ P({15}) = P({17}) = ²/ 16 NO P({18})= =
- The task is to implement density estimation using the K-NN method. Obtain an iidsample of N ≥ 1 points from a univariate normal (Gaussian) distribution (let us callthe random variable X) centered at 1 and with variance 2. Now, empirically obtain anestimate of the density from the sample points using the K-NN method, for any valueof K, where 1 ≤ K ≤ N. Produce one plot for each of the following cases (each plotshould show the following three items: the N data points (instances or realizations ofX) and the true and estimated densities versus x for a large number – e.g., 1000, 10000– of discrete, linearly-spaced x values): (i) K = N = 1, (ii) K = 2, N = 10, (iii) K = 10,N = 10, (iv) K = 10, N= 1000, (v) K = 100, N= 1000, (vi) K = N = 50,000. Pleaseprovide appropriate axis labels and legends. Thus there should be a total of six figures(plots),For following observations, fit a line y= a+bx by the method of least squares. Estimate the coefficients, assume that the observations are gathered randomly and independent from populations of normal distributions with constant Variance: x 0.34. 1.38. -0.65. 0.68. 1.40 y. 0.27. 1.34. -0.53. 0.35. 1.28 Continue… x -0.88. -0.3. -1.18. 0.5. -1.75 y -0.98. 0.72. -0.81. 0.64. -1.59Consider a test of H0 : μ ≤ 100 versus H1 : μ > 100. Suppose that a sample of size 20 has a sample mean of X = 105. Determine the p-value of this outcome if the population standard deviation is known to equal (a) 5 (b) 10
- Find the exact distribution for the Wilcoxon rank sum statistics W2 and U2 when n1 = 4, n2 = 2. Use this to find P (U2 ≤ 3) and P (U2 ≥ 8). calculate without using python codesin a trained a logistic regression classifier. it outputs a new example x with a prediction ho(x) = 0.3. This means: Select one: Oa. Our estimate for P(y-1 | x) Ob. Our estimate for Ply-0 | x) Oc. Our estimate for P(y-1 | x) Od. Our estimate for P(y=0 | x)Let X be a random variable with density function 1) ={0. k(1 -x), if 0<*<1; otherwise. f(x) Find k, together with the expectation and the variance of the random variable Y defined as Y = 3X - 1.