Question

1. Fit the data below to its best distribution. Write a short summary of the process. Use screen captures to document all steps taken and explain how you would interpret and apply the results. Note that you may copy the data from this assignment pane.

4.218513	5.457595	4.104833	5.66144	5.923793
5.72236	5.017972	4.342421	5.015709	4.963804
5.936002	4.441882	5.747402	5.616543	4.499608
4.541317	5.173397	4.930486	4.644949	4.28327
4.075418	5.901812	5.549519	4.112702	4.652694
4.884049	5.334384	5.106475	4.267806	4.008014
4.254265	4.987501	5.164127	5.216153	4.816361
5.289255	4.782876	5.679872	4.469803	4.127878
4.511913	5.186632	5.630699	4.345536	5.024503
4.114124	4.734761	5.251206	5.798727	4.802292

Answer 1

ANSWER::

2. Distributions A distribution is a linear map T : D(Ω) that R whidı is cntinuous in the sense D2) The space of distributions on Ω is denoted by D10). 3. Examples 3.1. Locally integrable functions Let fe L(2) be given. Then we define Tf E D(2) by setting Exercise 2. Show that Tr is a distribution, in particular verify the continuity condition Lemma 1. If f,g are locally integrable functions which are the same almost every- uhere, then Ty and Tg are the sme distribution Cornersely, if Tj =T, then f = g ae. Proof. For h-f -gwe have Th T -Tg 0, which means that h(x)p(r) dr 0 for all pe D(Q). This implies h(z) = 0 ae (1 postpone the proof of this statement to section 7.) 3.2. Dirac's delta function. The distribution defined by is called Dirac's delta function.