Problem $15.$ For the model in the shopping cart problem $($Problem $11),$ derive and plot the conditional mean squared error, as a function of the number on the observed cart, for the MAP, LMS$,$ and linear LMS estimators.

Problem $11.$ The number $$ of shopping carts in a store is uniformly distributed between $1$ and $100.$ Carts are sequentially numbered between $1$ and $.$ You enter

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Bayesian Statistical Inference

Chap. $8$

the store, observe the number $x$ on the first cart you encounter, assumed uniformly distributed over the range $1,$dots,$,$ and use this information to estimate $.$ Find and plot the MAP estimator and the LMS estimator. Hint: Note the resemblance with Example $8\mathrm{.}2.$ pls help problem $14$