How can I use R to compute confidence intervals for a Poisson distribution?

[Artusartos]

Suppose $$X_1, X_2, ... , X_10$$ is a random sample on a random variable X which has a Poisson distribution with mean $$\theta$$. Say the realized value of the sample mean is 0.5, i.e., $$n \bar{x} = 5$$. Suppose we want to compute the confidence interval $$(\bar{\theta}, \underline{\theta})$$. Using the table (for a poisson distribution), show that 0.2 and 0.3 bracket $$\underline{\theta}$$ and that 0.9 and 1.0 bracket $$\bar{\theta}$$. If R is available, us the R function poissonci.r to compute the solutions ot the equations.

I want to use R, but I'm not sure how...

I tried to put the commands:

$$poi(4, 10 \cdot 0.2)$$
$$poi(4, 10 \cdot 0.3)$$
$$poi(5, 10 \cdot 0.9)$$
$$poi(5, 10 \cdot 1.0)$$

...because that's what they do in my textbook. But, for some reason, I don't know how to type the dot (between 10 and 0.2 for example) in R...

So can anybody help me please?


Thanks in advance

 

[lippyka]

!You can use the poissonci.r function in R to compute the confidence interval. The syntax you need to use is: poissonci.r(n, xbar, level)where n is the sample size, xbar is the sample mean, and level is the desired confidence level. For your example, you would use:poissonci.r(10, 0.5, 0.95)This will return the lower and upper bounds of the 95% confidence interval for the mean, which should be 0.2 and 0.9 respectively.