Question

Three electron emitters produce electron beams with changing kinetic energies that are uniformly distributed in the ranges [7,8], [4,5), and [3,12]. Let Y denote the total kinetic energy produced by these electron emitters. (a) Suppose that the three beam energies are independent. Determine the mean and variance of Y. Round your answers to two decimal places (e.g. 98.76). Mean = Variance = (b) Suppose that the covariance between any two beam energies is -0.2. Determine the mean and variance of Y. Round your answers to two decimal places (e.g. 98.76). Mean = Variance = (c) Compare and comment on the results in parts (a) and (b): The covariance The covariance • mean. variance.

Answer 1

uniformly distri buted Elx) a+b Van()b-a 1 1a Giwen E,€ u53 3,12 a) Mean 7+8 4+5 3+12 24 2 15 15 + 2 2 Hean 19.5 Ce-7) 12-3) (5-4) Variance 4 12 12 J2 1 18 12 93 6.92 12 12 E(1)+E() +E()7-5+4-547- mean 19-5 Voi ()+ Vaon )+lo)2 Gov 1,) tariance + 2x Cov (1,,7) 2A 3 2 -0.2) t 12 6.92 +3* 2 o.2) 5.72 ( Variane elector emiler more than Coveriane veaianar mean tor to0 beun eneryies aule fane