The random variable ξ has a density function fξ(x) = = 0.5 · sin x in an interval (0, π). Outside of this interval fξ = 0 is valid. To find the mathematical expectation of η = ξ 2 . The random...

The random variable ξ has a density function fξ(x) = = 0.5 · sin x in an interval (0, π). Outside of this interval fξ = 0 is valid. To find the mathematical expectation of η = ξ 2 .

The random variable ξ has the density function fξ(x) = 2 cos 2x in an interval (0, π/4). Outside of this interval fξ(x) = 0 is valid. To find the mode and median of ξ.

The random variable ξ has a density function

To find the mathematical expectation and variance.

K e y. It is expedient to take the expression for the gamma-function