Example 2:Expectation,Mean,and Variance Let X be a random variable with PMF (x2 w- ifx=-3,-2,-1,0,1,2,3 otherwise .(c)Using the result from part(b),find the variance of X. 2 999 varX)=E☑]=1×i4+4×气+9 14= 14 Z 0 1 4 9 0 0 2×1/28 2×4/28 2×9/28 =1/14 =2/7 =9/14 10Example 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 • (c) Using the result from part (b), find the variance of 𝑋. 𝑣𝑎𝑟 𝑋 = 𝐸 𝑍 = 1 × 1 14 + 4 × 2 7 + 9 × 9 14 = 99 14 10 Z 0 1 4 9 P 0 2 × 1/28 = 1/14 2 × 4/28 = 2/7 2 × 9/28 = 9/14