Question

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 = 4.

(a) Compute E(X) and V(X). (Round your answers to four decimal places.)

E(X) =
V(X) =

(b) Compute P(X ≤ 0.4). (Round your answer to four decimal places.)


(c) Compute P(0.4 ≤ X ≤ 0.8). (Round your answer to four decimal places.)


(d) What is the expected proportion of the sampling region not covered by the plant? (Round your answer to four decimal places.)

Answer 1

Answer:

a)

Given,

f(x) = 1/() *x^-1 (1-x)^-1

Mean = / (+)

substitute values

= 5 / (5+4)

= 5/9

= 0.5555

Variance = / (+)^2*( + + 1)

= 20 / (9^2*(10))

= 0.0247

d)

Now the expected proportion of the sampling region not covered by the plant = 1 - E(X)

= 1 - 5/9

= 0.4444

Post the remaining two bits as separate post. Thank you.