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 $\alpha = 5$ and $\beta = 2$. (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = 0.7143 V(X) = 0.0255 (b) Compute P(X ? 0.5). (Round your answer to four decimal places.) 0.3633 (c) Compute P(0.5 ? X ? 0.9). (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.)

          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 $\alpha = 5$ and $\beta = 2$.
(a) Compute E(X) and V(X). (Round your answers to four decimal places.)
E(X) = 0.7143
V(X) = 0.0255
(b) Compute P(X ? 0.5). (Round your answer to four decimal places.)
0.3633
(c) Compute P(0.5 ? X ? 0.9). (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.)

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
V(X) = 0.0255
(b) Compute P(X ? 0.5). (Round your answer to four decimal places.)
0.3633
(c) Compute P(0.5 ? X ? 0.9). (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.)

Added by Alyssa C.

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