2 help please thank you Verify that the following function is a probability mass function, and determine the requested probabilities.f(x) = (216/43) (1/6)*, x = {1,2,3}Round your answers to four decimal places (e.g. 0.9876).Is the function a probability mass function?(a) P (X ≤ 1) = i(b) P(X > 1) =(c) P (2 < X < 10) =(d) P (X ≤ 2 or X > 2) =Statistical Tables and Cha

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 18E

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Repeat Example 1a for the function f(x)=2x2 on [1,2]. What is the probability that X will be between 32 and 2?
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.
Let X denote the number of hours you study during a randomly selected school day. The probability (pmf) that X can take the values x, has the following form, where k is some unknown constant. P(X = x) a. Complete the following table X P(X) b. Find the value of k. 0 0.1, if x = 0 kx, if x = 1 or 2 k(5-x), if x = 3 or 4 0, otherwise 1 2 3 4 c. What is the probability that you study at least two hours? d. What is the probability that you study exactly two hours? e. What is the probability that you study at most two hours? f. Compute the expectation E(X) g. Compute variance Var(X
A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?

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