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.)

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)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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

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