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In some settings there are not enough COED19 test kits and pooled testing is used in which multiple samples om di'erent people are combined in a \"pool.\" The pooled sample is tested, with two possibilities: 1. If negative, then all people in the pool are negative or 2. If the pool tests positive, then all people who contributed are tested individually Suppose there are N individuals in the targeted populaon to be tested and the unknown prevalence of Covinlg infection in this population be H. Suppose the N people in the population are split into if \"pools" with 1'1 people in each people soN=Knandn331 Let i"!- represent the number of assays required for 1: persons in pool ti = 112.3. ...K. Let T represent total assay required T = ELLE\":- 1. Find an expression for the expected number of assays in this population in terms of 211'. N. 3*! [Note: Use K = Min] 2. If R = E['i'],.l'l"v.|r is the ralio of expected number of assays needed wih pooling compared to assaying all N persons individually, calculate R assuming TE 2 l].l]l for n = ljll [Note: R should be independent of N] 3. Determine the optimal number of individuals to pool when a = [Illlll [ie. minimise R with it = [Llllll and nd it]