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Mathematical Methods in the Physical Sciences
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardFor a football game in the National Football League, let y = difference between the number of points scored by the home team and the away team (so y > 0 if the home team wins). Let x bet the predicted difference according to the Las Vegas betting spread. For the 768 NFL games played between 2003 and 2006, output follows. Predictor Coefficient SE Coef T P Constant -0.4022 0.5233 -0.77 0.442 BP 1.0251 0.0824 12.44 0.000 (a) We wish to test the null hypothesis that the Las Vegas predictions are unbiased. This will correspond with ? = 0 and ? = b) Based on the results shown in the table, is there much evidence that the sample fit differs from the model ?y = ? + ?x, with values of alpha and beta above? Why?arrow_forwardP(1.15 < Z < 2.77) =arrow_forward
- You collect data on 50 randomly selected individuals to determine how important income (x)is in determining charitable donations (y) by individuals. Income is measured in thousands of dollars and charitable donations is measured in dollars. You find the following. n n > Xiyi = 555525, > x; = 182985, = 2200040, i=1 i=1 i=1 What is the expected average increase in charitable donations given a ten thousand dollar increase in income? Select one: а. 0.1504 dollars O b. 1.5038 dollars С. 3.0415 dollars d. 4.2136 dollars e. 42.1359 dollarsarrow_forwardExponential Distribution has a memoryless property. Intuitively, it means that the probability of customer service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if you have waited an hour on the line or just picked up the phone. Formally, if X ∼ exponential(λ), f(x) = λ exp(-λx), and t and s are two positive numbers, use the definition of conditional probability to show that P(X > t + s | X > t) = P(X > s). Hint: Find the cdf of X first, and note that P(X > t + s Ç X > t) = P(X > t + s)arrow_forward%3D . If a and b are constants, then prove that expected value E[aX + b] = aE[X] + b.arrow_forward
- Solve these questions using the data table below pleasearrow_forwardP(z < 2.56) =arrow_forwardThe 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 %.arrow_forward
- Assuming the pmf is a valid one.arrow_forwardAssume x is exponentially distributed with a mean of 4. Find: a.P(X=2) b.P(X<2) c.P(X>=2) d.P(2 < X < 4)arrow_forward6:13 O .. Document (2) - Saving... Dr. Stoney has administered a test to his students. He calculated a X = 86 and Sx = 12. a. What is the z-score of a student with a raw score of 80? b. What is the raw score for a student with a z-score of -1.5? II B IU A = E E E 2arrow_forward
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