Math Q1 1. Let X have the probability density function f(x) = cr(1-x) for 0≤x≤ 1 and f(x) = 0 otherwise.(a) Show that c = 6.(b) Find the cumulative distribution function F(x)=P(X ≤r).(c) Calculate P(.1 < X < .5).(d) Find the mean, variance and standard deviation of X.

The probability density function of a random variable is given as,

Answered: 1. Let X have the probability density…

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.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 29CR

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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.
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1. Let X have the probability density function f(x) = cr(1-x) for 0 ≤x≤ 1 and f(x) = 0 otherwise. (a) Show that c = 6. (b) Find the cumulative distribution function F(x) = P(X ≤ x). (c) Calculate P(.1 < X <.5). (d) Find the mean, variance and standard deviation of X.