Introduction to Probability phần 7 docx

... .6 · 170 0 = 1020. The standard deviation for the number that accept is √ 170 0 · .6 · .4 ≈ 20. Thus we want to estimate the probability P (S 170 0 > 1060) = P (S 170 0 ≥ 1061) = P  S ∗ 170 0 ≥ 1060.5 ... .4332 2.5 .4938 3.5 .4998 .6 .22 57 1.6 .4452 2.6 .4953 3.6 .4998 .7 .2580 1 .7 .4554 2 .7 .4965 3 .7 .4999 .8 .2881 1.8 .4641 2.8 .4 974 3.8 .4999 .9 .3159 1.9 . 471 3...

Ngày tải lên: 09/08/2014, 23:20

... by a probability distribution on the set of states, which we will call a probability vector. A probability vector with r components is a row vector whose entries are non-negative and sum to 1. ... going to a certain four-year medical school in northern New England has, each year, a probability q of flunking out, a probability r of having to repeat the year, and a probability...

Ngày tải lên: 09/08/2014, 23:20

... with careful planning one would have to be extremely lucky to be able to stop so cleverly. The second author likes to trace his interest in probability theory to the Chicago World’s Fair of 1933 ... Morale,” p. 301. 7 ibid., pp. 277 – 278 . 8 N. T. Gridgeman, “Geometric Probability and the Number π” Scripta Mathematika, vol. 25, no. 3, (1960), pp. 183–195. 54 CHAPTER 2. CONT...

Ngày tải lên: 04/07/2014, 10:20

... 15 2556 16 2456 17 2 479 18 2 276 19 2304 20 1 971 21 2543 22 2 678 23 272 9 24 2414 25 2616 26 2426 27 2381 28 2059 29 2039 30 2298 31 2081 32 1508 33 18 87 34 1463 35 1594 36 1354 37 1049 38 1165 39 ... DENSITIES Female Male A 37 56 93 B 63 60 123 C 47 43 90 Below C 5 8 13 152 1 67 319 Table 5.8: Calculus class data. Female Male A 44.3 48 .7 93 B 58.6 64.4 123 C 42.9 47. 1 90 Belo...

Ngày tải lên: 04/07/2014, 10:20

... Logic, rev. ed. (New York: Academic Press, 1 977 ). 7. 2. SUMS OF CONTINUOUS RANDOM VARIABLES 2 97 Outcome Observed Frequency 1 15 2 8 3 7 4 5 5 7 6 18 Table 7. 1: Observed data. for moderate or large ... McGraw-Hill, 19 37) , p. 277 . 290 CHAPTER 7. SUMS OF RANDOM VARIABLES 6 People arrive at a queue according to the following scheme: During each minute of time either 0 or 1 per...

Ngày tải lên: 04/07/2014, 10:20

... Chebyshev 100 .3 173 1 1.00000 200 .1 573 0 .50000 300 .08326 .33333 400 .04550 .25000 500 .02535 .20000 600 .01431 .166 67 700 .00815 .14286 800 .00468 .12500 900 .00 270 .11111 1000 .001 57 .10000 Table ... <n, or     S n n     <. We wish to show that the probability of this event tends to 1 as n →∞, or equivalently, that the probability of the complementary event...

Ngày tải lên: 04/07/2014, 10:20

... -200 up H 28.8 25 to 200 2 O 29.4 25 to 200 2 H O(g)* 36.4 25 to 200 2 SO (g) 41.9 25 to 200 2 S (r) 23 .7 25 to 200 S (m) 25.9 95 to 120 *For rough calculations it is sufficient to set C (steam) ... be necessary to measure masses about a million times more accurately than is now possible to be able to determine energies to the accuracy required in thermochemistry. 7/...

Ngày tải lên: 08/08/2014, 15:21

... freezing of 5 g of supercooled water, at - 10 C, to ice at - 10 C, calculate o o a. ∆H b. ∆S c. ∆G 1 torr = 1 “mm of Hg” = 1 /76 0 atm = 133.3 Pa 2 7/ 10/ 07 3- 59 Escaping Tendency The thermodynamic ... and dilute solutions, are too important to permit such awkward behavior of the function chosen to describe them. We turn, therefore, for this purpose to the vapor pressure or to...

Ngày tải lên: 08/08/2014, 15:21

... law is not really applicable to solutions.) 7/ 10/ 07 3- 75 fraction of impurity in the water, is only 10 , the osmotic pressure is 1.38 x 10 Pa = 1.36 atm or -3 5 1032 torr. The effectiveness of ... and n and the integrated equation 1 2 3 divided by N to give the same result. 1 7/ 10/ 07 3- 72 and integration from pure solvent (N = N = 0) to dilute solution (N and N very small)...

Ngày tải lên: 08/08/2014, 15:21

... 2 1 1 RT TH N ∆∆ =∆ )( 111 BA HHH −=∆ 7/ 10/ 07 3- 83 15. The vapor pressures of benzene and toluene, at 27 C, are 120 and 40 torr. Assuming an ideal o solution, what is the composition ... (7) ln aRTGG o Q +∆=∆ ( ) (8) b B a A d D c C aa aa a =Q 7/ 10/ 07 4- 85 Subtraction of equation 2 from equation 1 gives At this point it is convenient to substitute the fugacities (equation 7a, ....

Ngày tải lên: 08/08/2014, 15:21