Set by Dr. Daniel Perley.

Just to cross-check my practice of this course work. Please post your answer with R command lines used.

Fit a generalized linear model to the data (https://1drv.ms/u/s!AgOhBzX2T2W6uyKl4Uu92IAjWLM8?e=FB5OSi), using an appropriate error family.Use a fourth degree polynomial for the linear predictor, and employ the canonical link function for this error family.Produce a new plot of the data, and add the model curve.

You are deciding between two hypotheses.Both are equally plausible.The first hypothesis (A) states that a distribution is normal with a mean of $\mu$=0 and a standard deviation of $\sigma$=1.The second hypothesis (B) states that the distribution is exponential with a rate parameter of $\lambda$=1.

1. You measure a value from the distribution and find it to be 1.3.Calculate the likelihood of this measurement if hypothesis A is true.

2. Calculate the likelihood of this same measurement if hypothesis B is true.

3. What is the probability that hypothesis A is the correct one, given this measurement and the assumptions stated above?

4. What is the odds ratio of the two hypotheses (A versus B), given this measurement?

5. You obtain a second measurement and find it to be 3.0.Provide an updated estimate of the probability that hypothesis A is the correct one, using all the information at hand.