Sumawith a Random Number of Terms following problems are a variation of Problem 5.11.139 in Wackerly, et al. Celelations

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Sumawith A Random Number Of Terms Following Problems Are A Variation Of Problem 5 11 139 In Wackerly Et Al Celelations 1 (71.27 KiB) Viewed 30 times

Sumawith a Random Number of Terms following problems are a variation of Problem 5.11.139 in Wackerly, et al. Celelations of this nature arise often in probability models and are represen- Estive of typical uses of the tower law to compute expectations. Let X1, X2,... be an infinite sequence of independent, identically distributed random variables with + E[X,] = 1x and var(x) = ož <co. You may assume for simplicity that the X;'s are discrete, although that's not really going to change anything. Let N be a random counting number with E[N] = un and var(N) = oŘ < x. Assume that N and the X's are mutually independent. Define S - ΣΧ. Problem 3. (a) (2 points) What is var(S|N = n) ? (b) (1 point) What is var(SIN)? (c) (1 point) What is Elvar(SIN)? (d) (1 point) What is var(ELSIN) (e) (1 point) What is var(5) Hint Use the ANOVA formula, tehich appears Threm 5.15 in Warkalica