1. Consider the simple pandemics model X+1 distributed over [e=1, e]. WkXk where {W1} is an i.i.d. sequence that is uniformly (a) Find the CDF and PDF of log Wk. (b) Find E[log Wk].

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1. Consider the simple pandemics model \( X_{k+1} = W_k X_k \) where \(\{W_k\}\) is an i.i.d. sequence that is uniformly distributed over \([e^{-1}, e]\).

   (a) Find the CDF and PDF of \(\log W_k\).

   (b) Find \(\mathbb{E}[\log W_k]\).
Transcribed Image Text:1. Consider the simple pandemics model \( X_{k+1} = W_k X_k \) where \(\{W_k\}\) is an i.i.d. sequence that is uniformly distributed over \([e^{-1}, e]\). (a) Find the CDF and PDF of \(\log W_k\). (b) Find \(\mathbb{E}[\log W_k]\).
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