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cory young

cory y.

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We often hear the phrase "law of averages," whi -ed to suggest happen to compensate for short-term results. For example, if a baseba strikeouts in a row, a sports commentator might naively state, "He is gambling context, we might hear someone say, "The roulette wheel h because of the law of averages." The common usage of this phrase is long term applied to the short term. For this exercise, consider the tos «Amazingly, suppose you get 10 heads on your first 10 tosses in front oi Ecoin 90 more times, and given the results of the first 10 tosses, how ma Your friend responds, "50 heads since the coin is fair." © Macmil Explain how your friend's incorrect answer most likely relates to t The friend thinks that the "law of averages" applies to known The friend's mistake is continuing to assume that the coin is fa and the friend isn't taking that into account when determining The friend thinks the "law of averages" only works for the

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According to John Bowe, in his book Nobodies, who is the devil?

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There is a uniform magnetic field of magnitude 2.7 T in the +z direction. a) What is the magnitude F1 of the force on a particle of charge -1.8 nC if its velocity is 1.4 km/s in the yz plane, in a direction that makes an angle of 34 with the z axis? b) What is the magnitude of F2 of the force on the same particle if its velocity is 1.4 km/s in the xy plane in a direction that makes an angle of 34 with the x axis?

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E6.7 Exercise. Let $f, g: \mathbb{R} \to \mathbb{R}$ be continuous functions such that $f(x) > g(x)$ for all $x \in \mathbb{R}$. Define subspaces $X, Y$ of $\mathbb{R}^2$ as follows. $X := \{(x, y) \in \mathbb{R}^2 \mid g(x) \le y \le f(x)\}$ $Y := \{(x, y) \in \mathbb{R}^2 \mid 0 \le y \le 1\}$ Show that $X \cong Y$.

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b.) The poor and working classes

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(a) Journalize the closing entries at April 30. (Credit account titles are automatically indented when amount is entered. Do not indent manually.) No. Date Account Titles and Explanation Debit Ci (1) Apr. 30 (2) Apr. 30 (To close revenue account) (To close expense accounts) (3) Apr. 30 (To close net income / (loss)) (4) Apr. 30 (To close dividends)

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3. [25 points] Suppose a music collection consists of 4 albums: the album Alina has 5 tracks; the album Bends has 12; the album Coieda has 15; and the album Debut has 12. (a) How many bits would be required to uniformly code: i. The index of all the albums? (We are not encoding the actual music, but merely the titles the metadata). Give an example uniform code for the albums. [2 points] ii. Only the tracks in the album Alina. Give an example of a uniform code for the tracks assuming they are named Track 1, Track 2, etc. [2 points] iii. All the tracks in the music collection? [2 points] (b) What is the raw bit content required to distinguish all the tracks in the collection? [2 points] (c) Suppose every track in the music collection has an equal probability of being selected. Let A denote the album title of a randomly selected track from the collection. i. Write down the ensemble for A, that is, its alphabet and probabilities. [2 points] ii. What is the raw bit content of A4? [2 points] iii. What is the smallest value of such that the smallest -sufficient subset of A4 contains fewer than 256 elements? [3 points] iv. What is the largest value of such that the essential bit content H(A) is strictly greater than zero? [4 points] (d) Suppose the album titles ensemble A is as in part (c) i. Compute an approximate value for the entropy H(A) to two decimal places (you may use a computer or calculator to obtain the approximation but write out the expression you are approximating). [2 points] ii. Approximately how many elements are in the typical set Tv for A when N = 100 and = 0.1? [2 points] iii. Is it possible to design a uniform code to send large blocks of album titles with [2 points]

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QUESTION 2 [20 MARKS] A 300 N 450 N B -400 mm- 200 mm -300 mm-200 mm 150 N 120mm h The shaft if it is subjected to the vertical loadings. The bearings at A and B exert only vertical reactions on the shaft. (a) Draw the shear-force diagram for the beam and loading shown. Determine the maximum absolute value of shear ($V_{max}$). [12 marks] (b) Determine the height of the beam, h if the allowable shearing stress for the beam is 0.9MPa. [8 marks]

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Problem 33 Let {et, -o< t < oo} be iid random variables with Ee; =0 and Ee= o2. Compute the spectral density of 1737+73=?

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$V(x) = \begin{cases} +\infty & x \leq 0 \\ \frac{1}{2}m\omega^2 x^2 & x > 0 \end{cases}$

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