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Sagot :
Answer:
Step-by-step explanation:
From the given information:
Note that the possible values of Y are 0 and 1 because;
y = 0 if X = 0 and y = 1 if X = ±1
∴
[tex]P(Y =0) = P(X = 0) =\dfrac{1}{3}[/tex]
[tex]P(Y = 1) = P(X = -1 \ or \ 1) \\ \\ = P(X = -1) + P(X = 1)[/tex]
[tex]= \dfrac{1}{2}+ \dfrac{1}{6}[/tex]
[tex]=\dfrac{3+1}{6}[/tex]
[tex]= \dfrac{2}{3}[/tex]
b)
[tex]E(|X|) = \sum |x| P(X=x) = ( 1 \times \dfrac{1}{2}) + ( 0\times \dfrac{1}{3}) + ( 1 \times \dfrac{1}{6})[/tex]
[tex]= \dfrac{2}{3}[/tex]
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