Suppose the proportion X of surface area in a randomly selec

Suppose the proportion X of surface area in a randomly selected square region that is covered by a certain plant has a beta distribution with parameters = 5, = 2.

a)Graph the probability density function f(x).

b)Compute the expected valueE(X)= and standard deviation V(X)=.

c)Compute the probability that X is less than 0.20. Solve this question by hand.

d)Compute the probability that X is between 0.20 and 0.40. Solve this question using “pbeta” in R.

e)What is the expected proportion of the sampling region not covered by the plant?

Solution