Suppose the Proportion X of Surface Area in a Randomly $\alpha = 5 \text { and } \beta = 2$

question 10

Essay

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 $\alpha = 5 \text { and } \beta = 2$
a. Compute E(X) and V(X).
b. Compute $P ( X \leq 2 )$
c. Compute $P ( .2 \leq X \leq 4 )$
d. What is the expected proportion of the sampling region not covered by the plant?

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