Suppose the proportion X of surface area in a randomly selected square region th

Question

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?

Explanation / Answer

Suppose the proportion X of surface area in a randomly selected square region th

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