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- Let X have the Pareto distribution with parameter a > 0. The Pareto PDF isfX (x) = a/x^a+1 if x ≥ 1 0 otherwise.(a) Find all medians of X.(b) Find all modes of X.If a continuous RVX (> 0) possesses memoryless property, that is P(X>x+h)= P(X>x). P(X > h), then X follows an exponential distribution.A random variable X follows the continuous uniform distribution with a lower bound of - 7 and an upper bound of 16 What is the height of the density function f(x)? What are the mean and standard deviation of this distribution?
- If the probability density of a random variable is given by fx(x) = K(1-x²) 0What is the variance of a continuous probability distribution given by the density function f(x) = 4x(1-x) for 0 < x < 1?The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of $131. The lambda of this distribution is The probability that the cost is larger than $157 is P(x ≥ $157) = The probability that the cost is less than $97 is P(x ≤ $97) = The probability that the cost is between $121 and $143 is P($121 ≤ x ≤ $143) = The 20th percentile is cost of maintenance $Let f, g be probability densities such supp(f) c supp(g). show yes i.i.d. X1,..., X, L(g) then f(X;) Wi 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.One of the important properties of the probability density function , f(x) , of a random variable X is f(x) >= 0 , for all values of X. A) true B) falseShow that the Cauchy probability distribution does not have the first moment that is, E(X) does not exist.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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