Course: Statistics The manager of a company has determined that the quantity function that determines the probability of closing a business is determined by the function f(x)=3x2, with x ∈ [0;1]. Determine the mathematical expectation of this function. Select one: a. A expectation of 0.75% is estimated b. A expectation of 75 percent is estimated c. Estimated expectation is 7.5%. d. Estimated expectation of 0.75 e. Estimated expectation of 1

Course: Statistics The manager of a company has determined that the quantity function that determines the probability of closing a business is determined by the function f(x)=3x2, with x ∈ [0;1]. Determine the mathematical expectation of this function. Select one: a. A expectation of 0.75% is estimated b. A expectation of 75 percent is estimated c. Estimated expectation is 7.5%. d. Estimated expectation of 0.75 e. Estimated expectation of 1

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.

Chapter9: Multivariable Calculus

Section9.4: Total Differentials And Approximations

Problem 23E: Eastern Hemlock Ring shake, which is the separation of the wood between growth rings, is a serious...

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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.
The equation below estimates the effect of race on the probability of mortgage denial, holding constant the payment-to-income ratio. Pr(deny = 1|P/I ratio, black) = 0(-2.21 + 2.73P/I ratio + 0,75black) %3! (0.16) (0.45) (0.085) A black mortgage applicant has a PA ratio of 0.39. What is the predicted probability that his application will be denied? The predicted probability that his application will be denied is 34.64 %. (Express your response as a percentage and round to two decimal places) o Suppose that the applicant reduced this ratio to 0.31. What effect would this have on his predicted probability of being denied a mortgage? The predicted probability of being denied a mortgage would decrease by 7.67 percentage points. (Round your response to two decimal places) ck A white mortgage applicant has a P/I ratio of 0.36. What is the predicted probability that his application will be denied? on The predicted probability that his application wil be denied is%. ory (Express your response…
The 2010 U.S. Census found the chance of a household being a certain size. The data is in the pmf below ("Households by age," 2013). Let X be the number (size) in a household. E(X) = k·P(X = k) 7 (or more) P(X=k) 0.267 0.336 0.158 0.137 0.063 0.024 0.015 k 1 2 3 5 6 a) The probability of a household size being more than 5, P(X > 5) = % b) In the long run, we are expected to see a household size of, E(X)= on average. Round answer to three decimal places. c) The probability that the size of a household is equal to two is %. d) The probability of a household size being three OR six is %.
The equation below estimates the effect of race on the probability of mortgage denial, holding constant the payment-to-income ratio. Pr (deny=1|P/I ratio, black) =(-2.29+2.78P/I ratio +0.71 black) (0.16) (0.46) (0.087) A black mortgage applicant has a P/l ratio of 0.38. What is the predicted probability that his application will be denied? The predicted probability that his application will be denied is%. (Express your response as a percentage and round to two decimal places)
Highway engineers use f(x) = (0.905)* to estimate the likelihood, or probability, that no vehicle will enter a particular intersection within an interval of x seconds. Construct a table of f(x) = (0.905)* starting at x = 0 and incrementing by 10, until x = 50. a. Evaluate f(1) and interpret the result. b. For a time interval of what length is there only a 2% chance that no cars will enter the intersection?
Use the information to answer the following questions. To calculate the risk premium on government bonds we use the formula. (1 + i) = (1 – p) (1 + i + x) + p(0) Where p is the probability that the bond does not pay at all (the bond issuer is bankrupt) and has a zero return, i is the nominal policy interest rate and x is the risk premium. a. If the probability of bankruptcy is zero, what is the rate of interest on the risky bond? (1) b. Calculate the probability of bankruptcy when the nominal interest rate for a risky borrower is 8% and the nominal policy rate of interest is 3%. (3) c. Calculate the nominal
If i have a function, what does it mean to "Take expectation" of it. Can you give and example and show how it is done
There is the sale of two types of candy bars which have the profit $0.85 and $ 1.75 per bar respectively. Furthermore, the supplier offers an incentive of $0.75 if the total candy bars sold exceeds 1,500. Determine the function where p equals the profit and Xj equals the number of bar sold each type. If 550 and 750 bars are sold respectively, what is the expected profit? If 900 and 1150 are sold, what is the expected profit?
The length X to complete a certain key task in house construction is exponentially distributed with mean of 5 hours. The cost of completing this task is C= 10+20X2. Find the expected cost. Select one: Oa. 1000 Ob. 1010 O c. 510 O d. 500
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
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Suppose that 95% of the bags of certain fertilizer mix weigh between 49 and 53 pounds. Averages of three succesive bags were plotted, and 47.5% of these were observed to lie between 51 and X pounds. Estimate the value of X. State assumptions you make and say whether these assumptions are likely to be true for this example.