Let X be a random variable with the probability density function Find (i) Value of a f(x): x) = { ›={ ae; x>0 0 ; otherwise
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- Let f, g be probability densities such supp(f) c supp(g). show yes X1, ... , Xn X1,..., X, iid. L(g) then f(X;) W; = g(X;) is hopeful 1. Argue why the weights need to be re-normalized even when the normalization constants of the densities f and g are known.Please helpA continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density function
- The probability density function for the continuous random variable X is given by: (А(х? — 2х + 21) 0Consider the probability density fx (x) = a. eb x! where X is random variable whose allowable values range from x = -o to + o. Find (a) the CDF (b) the relation between a and b (c) the probability that x lies between 1 and 2.Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.A machine has a useful life of 4 to 9 years, and its life (in years) has a probability density function defined by f(x) = 1 1 Find the probability that the useful life of such a machine selected 15 at random will be longer than 7 years?Let X will be continuous random variable with probability density function as below. f(x) = {4x , (0Let X be a random variable that follows the beta distribution. This random variable is continuous and is defined over the interval from 0 to 1. The probability density function is given by whereand are integers, whose values determine the shape of the probability density function. Because X varies between 0 and 1, we can think of X as the probability that some event (say) E occurs or the proportion of times an event occurs in some population. For example, E could denote the event that a critical part in a newly designed car will lead to a catastrophic failure in accidents at high speeds. The expected value (i.e., mean) of this random variable is []. That is, . The Excel commands for the beta random variable are =beta.dist(x,,,true,0,1) for the cumulative probability distribution, and =beta.dist(x,,,false,0,1) for the probability density function. (a) Now, think in Bayesian terms.…Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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