Problem $4\mathrm{.}7$ We define relative bias as the ratio between bias and the difference between the mean

of the stimulus distribution and the true stimulus.

a$)$ For the posterior mean estimate, derive an expression for relative bias as a function of the

ratio $R-=\frac{}{{}_s}.($Hint: the expression will only contain $R,$ no other variables.$)$

b$)$ Plot relative bias as a function of $R.$

c$)$ Does this plot show what you would expect from the Bayesian observer? Explain intuitively.