Assume that a random variable, x, is governed by the probability distribution (a version of the Lorentzian function) where x ranges from 10 000 to 10 000 (a) Find the mean value of x and its variance and standard deviation (b) Find the probability that x lies between copy x ordf Iuml x and copy x ordf Iuml x f (x) x2 4'

Question: Assume that a random variable, x, is governed by the probability distribution (a version of the Lorentzian function) where x ranges from 10.000 to 10.000.

Assume that a random variable, x, is governed by the probability distribution (a version of the Lorentzian function)

f (x) = x2 +4'

where x ranges from ˆ’10.000 to 10.000.
(a) Find the mean value of x and its variance and standard deviation.
(b) Find the probability that x lies between Œ©xŒª ˆ’Ïƒ_x and Œ©xŒª +Ïƒ_x.

f (x) = x2 +4'

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