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 a = 4 and (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = 0.5714 V(X) = 0.0306 (b) Compute P(X < 0.4). (Round your answer to four decimal places.) 0.1792 (c) Compute P(0.4 < X < 0.6). (Round your answer to four decimal places.) 0.4192 (d) What is the expected proportion of the sampling region not covered by the plant? (Round your answer to four decimal places.)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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 a = 4 and ß = 3
(a) Compute E(X) and V(X). (Round your answers to four decimal places.)
E(X) = 0.5714
V(X) = 0.0306
(b) Compute P(X < 0.4). (Round your answer to four decimal places.)
0.1792
(c) Compute P(0.4 < X < 0.6). (Round your answer to four decimal places.)
0.4192
(d) What is the expected proportion of the sampling region not covered by the plant? (Round your answer to four decimal places.)
0.4286
Transcribed Image Text: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 a = 4 and ß = 3 (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = 0.5714 V(X) = 0.0306 (b) Compute P(X < 0.4). (Round your answer to four decimal places.) 0.1792 (c) Compute P(0.4 < X < 0.6). (Round your answer to four decimal places.) 0.4192 (d) What is the expected proportion of the sampling region not covered by the plant? (Round your answer to four decimal places.) 0.4286
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