Determine the density of the distribution of a random variable X , draw the graphs of the density and the distribution and calculate E(2X +5),D²(X+3) EX, DX, P ( – 0,5

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Task 3 A random variable X has a distribution of the form:
for xE(-0, - 1)
(x+1)² for XE[-1,0)
4
F(x) =
3
1
for
XE[0, 2)
4
1
for
XE[2, +)
Determine the density of the distribution of a random variable X , draw the graphs of the density and
the distribution and calculate E(2X +5), D²(X+3) EX, DX, P ( – 0,5<X<0, 5), P(X=0, 25) the
moments of the ordinary and central order 3.
Transcribed Image Text:Task 3 A random variable X has a distribution of the form: for xE(-0, - 1) (x+1)² for XE[-1,0) 4 F(x) = 3 1 for XE[0, 2) 4 1 for XE[2, +) Determine the density of the distribution of a random variable X , draw the graphs of the density and the distribution and calculate E(2X +5), D²(X+3) EX, DX, P ( – 0,5<X<0, 5), P(X=0, 25) the moments of the ordinary and central order 3.
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