\begin{tabular}{|c|c|} \hline Lues & \\ \hline Beta & 1.48593777681193 \\ \hline ES95 & 0.229703928664163 \\ \hline ES99 & 0.229703928664163 \\ \hline ES99_Emp & 0.229703928664163 \\ \hline ES99_Norm & 0.394743329454835 \\ \hline & -0.0405120098260071 \\ \hline n & \( 10 \mathrm{~L} \) \\ \hline p & -1.95996398454005 \\ \hline Pa_daily_wide_ts & 'zoo' num [1:2516, 1:3] NA NA NA NA NA NA NA NA NA NA .... \\ \hline R & -0.15 \\ \hline Ra_yearly_weights & Named num \( [1: 3] \quad 0.3330 .3330 .333 \) \\ \hline Ra_yearly_wide_ts & 'zoo' num \( [1: 10,1: 3] \) NA \( -0.3250 .153-0.282-0.513 \ldots \) \\ \hline Rb_yearly_ts & 'zoo' num [1:10] 0.12387 -0.00727 0.095350 .1942 -0.062... \\ \hline \( \mathrm{Rf} \) & 0.03 \\ \hline \( \mathrm{Rm} \) & 0.147 \\ \hline \( \mathrm{s} \) & 0.163309701696087 \\ \hline Sm & 0.1215 \\ \hline times & Date[1:10], format: "2014-12-31" "2015-12-31" "2016-12-... \\ \hline VaR95 & Named num 0.183 \\ \hline VaR99 & Named num 0.22 \\ \hline VaR99_BT_Exp & 0 \\ \hline VaR99_BT_Obs & \( 0 \mathrm{~L} \) \\ \hline VaR99_Emp & Named num 0.22 \\ \hline VaR99_Norm & 0.339403167524928 \\ \hline \( \mathrm{x} \) & int [1:10] 12345678910 \\ \hline \( \mathrm{y} \) & num \( [1: 10]-0.537-0.1834-0.2076 \quad 0.2866 \quad 0.0652 \) \\ \hline yearly_Ret_ts & 'zoo' num [1:10, 1:5] NA -0.325 \( 0.153-0.282-0.513 \) \\ \hline \end{tabular}
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"Dalmatian Darnation," by Kathy Sparling A greedy dog breeder named Spreckles Bred puppies with numerous freckles The Dalmatians he sought Possessed spot upon spot The more spots, he thought, the more shekels. His competitors did not agree That freckles would increase the fee. They said, “Spots are quite nice But they don't affect price; One should breed for improved pedigree.” The breeders decided to prove This strategy was a wrong move. Breeding only for spots Would wreak havoc, they thought. His theory they want to disprove. They proposed a contest to Spreckles Comparing dog prices to freckles. In records they looked up One hundred one pups: Dalmatians that fetched the most shekels. They asked Mr. Spreckles to name An average spot count he'd claim To bring in big bucks. Said Spreckles, “Well, shucks, It's for one hundred one that I aim.” Said an amateur statistician Who wanted to help with this mission. “Twenty-one for the sample Standard deviation's ample: They examined one hundred and one Dalmatians that fetched a good sum. They counted each spot, Mark, freckle and dot And tallied up every one. Instead of one hundred one spots They averaged ninety six dots Can they muzzle Spreckles’ Obsession with freckles Based on all the dog data they've got?
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Flight formula for Indian spotted owlets The following table shows the average body mass $m(t)$ (in $g$ ) and average wing chord length $w(t)(\text {in } m m),$ along with the derivatives $m^{\prime}(t)$ and $w^{\prime}(t),$ of $t-$week-old Indian spotted owlets. The flight formula function $f(t)=w(t) / m(t)$ which is the ratio of wing chord length to mass, is used to predict when these fledglings are old enough to fly. The values of $f$ are less than $1,$ but approach 1 as t increases. When $f$ is close to $1,$ the fledglings are capable of flying, which is important for determining when rescued fledglings can be released back into the wild. (Source: ZooKeys, 132,2011 ) $$\begin{array}{lrrrr} t & m(t) & m^{\prime}(t) & w(t) & w^{\prime}(t) \\ \hline 1 & 23.32 & 41.45 & 10.14 & 14.5 \\ 1.5 & 50.59 & 64.94 & 20.13 & 26.17 \\ 2 & 82.83 & 57.95 & 36.7 & 39.86 \\ 2.5 & 105.13 & 31.08 & 58.92 & 47.11 \\ 3 & 115.48 & 12.48 & 81.55 & 41.38 \\ 3.5 & 119.4 & 4.44 & 98.99 & 27.94 \\ 4 & 120.76 & 1.51 & 109.75 & 15.74 \\ 4.5 & 121.22 & 0.51 & 115.5 & 7.99 \\ 5 & 121.37 & 0.17 & 118.34 & 3.85 \\ 5.5 & 121.42 & 0.06 & 119.69 & 1.8 \\ 6 & 121.44 & 0.02 & 120.32 & 0.84 \\ 6.5 & 121.45 & 0.01 & 120.61 & 0.38 \end{array}$$ State the units associated with the following derivatives and state the physical meaning of each derivative. a. $m^{\prime}(t)$ b. $w^{\prime}(t)$ c. $f^{\prime}(t)$
Derivatives
The Product and Quotient Rules
.00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 .1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753 .2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141 .3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517 .4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 .5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 .6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2517 .2549 .7 .2580 .2611 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852 .8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133 .9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389 1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621 1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015 1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177 1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545 1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633 1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706 1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767
Umar Sohail Q.
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