Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with α = 5 and β = 2. (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = 0.7143 Correct: Your answer is correct. V(X) = 0.02551 Correct: Your answer is correct. (b) Compute P(X ≤ 0.3). (Round your answer to four decimal places.)

a)

b) > pbeta(0.3,5,2,TRUE)

[1] 0.007885565

And as we can see we got 0.007885565

Step-by-step explanation:

For this case we have defined the random variable X ="surface area in a randomly selected quadrant that is covered by a certain plant", and we know the distribution for X

Part a

For this case we want to find the expected value and the variance for X.

The expected value is given by:

And the variance is given by:

And replacing we got:

Part b

For this case we want the following probability:;

For this case we can calculate the regularized incomplete beta function

Where is given by:

Replacing we got:

We can calculate the probability with the following R code:

> pbeta(0.3,5,2,TRUE)

[1] 0.007885565

And as we can see we got 0.007885565

sine

step-by-step explanation: