If the mean and variance of the frequency distribution x i 2 4 6 8 10 12 14 16 f i 4 4 α 15 8 β 4 5 are 9 and 15 . 08 respectively, then the value of α 2 + β 2 - α β is _____.

Step-by-step solution

Given, The mean and variance of the frequency distribution x i 2 4 6 8 10 12 14 16 f i 4 4 α 15 8 β 4 5 are 9 and 15 . 08 respectively, Now mean is given by, Mean = 8 + 16 + 120 + 80 + 56 + 80 + 6 α + 12 β 40 + α + β = 9 ⇒ 360 + 9 α + 9 β = 360 + 6 α + 12 β ⇒ 3 α - 3 β = 0 ⇒ α = β   . . . . . . 1 Now variance is given by, 15 . 08 = 16 + 64 + 36 α + 960 + 800 + 144 α + 784 + 1280 40 + 2 α - 9 2 ⇒ 96 . 08