Example 2:Expectation,Mean,and Variance Let X be a random variable with PMF (x2 Px(x)= ifx=-3,-2,-1,0,1,2,3 (0, otherwise ·(a)Find a and E[X] a=∑x2=2×(1+4+9)=28 X二-3 X=-3 8Example 2: Expectation, Mean, and Variance • Let 𝑋 be a random variable with PMF 𝑝𝑋 𝑥 = ൞ 𝑥 2 𝑎 , 𝑖𝑓 𝑥 = −3, −2, −1,0,1,2,3 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 • (a) Find 𝑎 and 𝐸[𝑋] 𝑎 = ෍ 𝑥=−3 3 𝑥 2 = 2 × 1 + 4 + 9 = 28 𝐸 𝑋 = ෍ 𝑥=−3 3 𝑥 ∙ 𝑥 2 28 = 0 8