Example 1 Let X be uniformly distributed in the unit interval 0,1.Consider the random variable Y=g(),where g)= ifx≤2/3， 2 ifx>2/3. Find the expected value of Y. X [0,2/3] Y 1 2 P 2/3 1/3 2 14 EY]=1× +2×3=3 9Example 1 • Let 𝑋 be uniformly distributed in the unit interval [0,1]. Consider the random variable 𝑌 = 𝑔(𝑋), where 𝑔 𝑥 = ቊ 1, 𝑖𝑓 𝑥 ≤ 2/3, 2, 𝑖𝑓 𝑥 > 2/3. • Find the expected value of 𝑌. 𝐸 𝑌 = 1 × 2 3 + 2 × 1 3 = 4 3 9 X [𝟎, 𝟐/𝟑] ( 𝟐 𝟑 , 𝟏] Y 1 2 P 2/3 1/3