Please use Rstudio

Question 4 Consider a variable X known to have a Poisson distribution. We will consider a null hypothesis that A = 3.1 (this question will consider one-sided tests only). Suppose we observe X = 7. . State the precise definition of p-value for our observation of 7 events . Calculate the p-value for this observation and interpret . For the observation of 7 events, plot a likelihood function for A, choosing a sensible range. . Again for the observation of 7 events, plot a log-likelihood function for A, and estimate a credible interval for A. A rough estimate is fine. . (harder) A Bayesian comes along and announces that his prior for A is an exponential distribution with rate 0.6 (that is, P(A) oc e-0.61). Plot his posterior likelihood function for A, given the observation of 7. (hint: you can calculate the density of the exponential distribution using dexp (x, rate=0.6)). . Give an example of observations drawn from a Poission distribution in your daily life. Give either a confidence interval or credible interval [hint: credible intervals are much easier] for the mean of your observations