Example 2: Consider the following function shown below, Use it to answer the followingquestions.x3P(x) =9'x = 0,1,2a) Determine whether or not the function shown above is a valid probability function.b) Construct a probability histogram for the function shown above and comment on theshape.domyec) Find P(x > 1)

Answered: Example 2: Consider the following…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.CR: Chapter 12 Review

Problem 11CR

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Eastern Hemlock Ring shake, which is the separation of the wood between growth rings, is a serious problem in hemlock trees. Researchers have developed the following function that estimates the probability P that a given hemlock tree has ring shake: P(A,B,D)=11+e3.680.016A0.77B0.12D where A is the age of the tree yr, B is 1 if bird pecking is present and 0 otherwise, and D is the diameter in. of the tree at breast height. Source: Forest Products Journal. a. Estimate the probability that a 150-year-old tree with bird pecking present and a breast height diameter of 20in., will have ring shake. b. Estimate the probability that a 150-year-old tree, with no presence of bird pecking and a breast height diameter of 20in., will have ring shake. c. Develop a statement about what can be said about the influence have on the probability of ring shake. d. Using the total differential, estimate the probability if the actual age of the tree was 160 years and the diameter at breast height was 25in., Assume that no bird pecking was present. Compare your answer to the actual value. Hint: Assume that B=0 and exclude that variable from your calculations e. Comment on the practicality of using differentials in part d.
Repeat Example 1a for the function f(x)=2x2 on [1,2]. What is the probability that X will be between 32 and 2?
Determine if the statement is true or false. If the statement is false, then correct it and make it true. The probability that an event occurs can be a negative number.

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Example 2: Consider the following function shown below. Use it to answer the following questions. P(x) = x = 0,1,2 a) Determine whether or not the function shown above is a valid probability function. b) Construct a probability histogram for the function shown above and comment on the shape.