Problem $3\mathrm{.}5$ The figure below shows a likelihood function and a posterior distribution. Both are Gaussian, with ${}_{\text{p}\text{o}\text{s}\text{t}\text{e}\text{r}\text{i}\text{o}\text{r}}=1\mathrm{.}2$ and ${}_{\text{l}\text{i}\text{k}\text{e}\text{l}\text{i}\text{h}\text{o}\text{o}\text{d}}=1\mathrm{.}5.$ Assume that the prior is also Gaussian. Which of the following statements is true? Explain. You will need both the plot and the given numbers.

a$)$ The prior is centered to the left of the likelihood function and is narrower.

b$)$ The prior is centered to the left of the likelihood function and is wider than it$.$

c$)$ The prior is centered to the right of the likelihood function and is narrower than it$.$

d$)$ The prior is centered to the right of the likelihood function and is wider than it$.$