R Assistance

1. To compute Pr(X = x) using the binomial with n trials and p, the probability of

success, use the command dbinom(x,n,p) at the R prompt. For example, Pr(X = 3)

with n = 5; p = 0:6 is dbinom(3,5,0.6) = 0.3546.

2. To compute the Pr(X x) using the binomial with n trials and p, the probability of

success, use the command pbinom(x,n,p) at the R prompt. For example, Pr(X 3)

with n = 5; p = 0:6 is pbinom(3,5,0.6) = 0.66304.

3. To nd Pr(X > x) you can use the complement of 1 Pr(X x) and the above

commands.

4. To compute Pr(X = x) using the Poisson with average rate of success, use the

command dpois(x,mu) at the R prompt. For example, Pr(X = 3) with = 5 is

dpois(3,5) = 0.1403739.

5. To compute the Pr(X x) using the Poisson with average rate of success, use

the command ppois(x,mu) at the R prompt. For example, Pr(X 3) with = 5 is

ppois(3,5) = 0.2650259.

6. To nd Pr(X > x) you can use the complement of 1 Pr(X x) and the above

commands.

3.

In a study of drug-induced anaphylaxis among patients taking rocuronium

bromide as part of their anesthesia, Laake and Rottingen found that the occurrence

of anaphylaxis followed a Poisson model with = 12 incidents per year in Norway.

Answer the following:

(a) Find the probability that in the next year, among patients receiving rocuronium,

exactly three will experience anaphylaxis.

(b) What is the probability that at least three patients in the next year will experience

anaphylaxis if rocuronium is administered with anesthesia?

(c) What is the probability that between 10 and 15 patients, inclusively, will have

anaphylaxis? (must use 2 commands in R to get the answer and adding them is

not the answer, you will need to subtract them!)

4.

In the study of a certain aquatic organism, a large number of samples were

taken from a pond, and the number of organisms in each sample was counted. The

average number of organisms per sample was found to be two. Assuming that the

number of organisms follows a Poisson distribution, answer the following:

(a) What is the probability that in the next 3 samples taken will contain one or fewer

organisms?

(b) What is the probability that in the next 3 samples taken will contain exactly

three organisms?

(c) What is the probability that in the next 3 samples taken will contain more than

ve organisms?