Homework #11

EE 364: Spring 2026

ImportantAssignment Details

Assigned: 23 April
Due: Thursday, 30 April at 16:00

BrightSpace Assignment: Homework 11

WarningInstructions

Write your solutions to these homework problems. Submit your work to BrightSpace by the due date. Show all work and box answers where appropriate. Do not guess.

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Problem 0

Daily derivation #11

• Derive the mean and variance of a doubly random sum \(S_N = \sum_{k=1}^{N} X_k\), where \(X_1, \ldots, X_n\) are i.i.d. for all \(n\) with \(\sigma_X^2 < \infty\), and \(N\) is a positive integer-valued random variable independent of the \(X_k\): \[E\!\left[\sum_{k=1}^{N} X_k\right] = E_N[N]\,\mu_X \qquad V\!\left[\sum_{k=1}^{N} X_k\right] = E_N[N]\,\sigma_X^2 + V_N[N]\,\mu_X^2\]