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- Find the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln (1-U), where U ~ U (0,1) and λ> 0.Suppose that X is a continuous unknown all of whose values are between -3 and 3 and whose PDF, denoted f , is given by f ( x ) = c ( 9 − x^2 ) , − 3 ≤ x ≤ 3 , and where c is a positive normalizing constant. What is the variance of X?Derive a general expression for the variance of net future loss Var(L) with a constant force of interest δ under each of the following models:i. μ_x(t) = μii. μ_x(t) = 1/(ω-x)
- If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.If X is a uniformly distributed random varibale with a=9 and b=16, then Calculate the variance of X? Round to three decimal places1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.
- If the probability mass function of the variable X described in the table is. find variance Y=x^2+4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.85Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?
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