#+TITLE: Org-Flashcards Demo File
#+STARTUP: latexpreview

#+ATTR_LATEX: :scale 2 <- only helpful for export to latex!
#+ATTR_LATEX: :width 5cm 


* Moment Generating Function                                             :fc:
:PROPERTIES:
:ID:       2ffc8b34-b2b5-4472-9295-714b5422679d
:FC_CREATED: 2021-11-30T01:46:02Z
:FC_TYPE:  normal
:FC_ALGO:  noop
:END:
:REVIEW_DATA:
| position | due                  |
|----------+----------------------|
|        0 | 2000-01-01T00:00:00Z |
|        1 | 2000-01-01T00:00:00Z |
|        2 | 2000-01-01T00:00:00Z |
:END:
Define the moment generating function
** Back

\[ M_X(t) := \mathbb{E}\!\left[e^{tX}\right], \quad t \in \mathbb{R}\]

Differentiating $M_X(t)$ $i$ times with respect to $t$ and setting $t=0$ we obtain the $i\textup{th}$ moment.


* my card                                                                :fc:
:PROPERTIES:
:FC_CREATED: 2025-11-13T11:20:05Z
:FC_TYPE:  normal
:FC_ALGO:  sm2
:ID:       8E9EB629-0EA6-46E4-8B25-1BC3111C9EA0
:END:
:REVIEW_DATA:
| position | ease | box | interval | due                  |
|----------+------+-----+----------+----------------------|
| front    | 2.50 |   0 |     0.00 | 2025-11-13T11:25:12Z |
:END:

back



* Cloze Enumeration                                                      :fc:
:PROPERTIES:
:FC_CREATED: 2000-01-01T00:00:00Z
:FC_TYPE:  cloze
:FC_ALGO:  noop
:ID:       5eac5801-0ef5-4957-a818-e3f9f08a7d59
:FC_CLOZE_MAX: 3
:FC_CLOZE_TYPE: enumeration
:END:
:REVIEW_DATA:
| position | due                  |
|----------+----------------------|
|        0 | 2000-01-01T00:00:00Z |
|        1 | 2000-01-01T00:00:00Z |
|        2 | 2000-01-01T00:00:00Z |
|        3 | 2000-01-01T00:00:00Z |
:END:

Enumerations are useful for

- {{Learning}@0}
- {{Lists}@1}
- {{of}@2}
- {{items}@3}

* AWK Source Example                                                     :fc:
:PROPERTIES:
:FC_CREATED: 2000-01-01T00:00:00Z
:FC_TYPE:  cloze
:FC_ALGO:  noop
:FC_CLOZE_MAX: 2
:FC_CLOZE_TYPE: single
:ID:       ae675e11-e003-4057-b6b1-1f4702837502
:END:
:REVIEW_DATA:
| position | due                  |
|----------+----------------------|
|        0 | 2000-01-01T00:00:00Z |
|        1 | 2000-01-01T00:00:00Z |
|        2 | 2000-01-01T00:00:00Z |
:END:
#+begin_src awk
  # Set up variables for new file
  {{BEGINFILE}@0} {
      title = FILENAME;
  }

  match($0, /#\+TITLE: (.*)/, a) {
      title = a[1];
  }

  {
      i += 1;
      if (i > 5) {
          # Continue with next file
          {{nextfile}@1};
      }
  }

  # Print results for file
  {{ENDFILE}@2} {
      print FILENAME, title;
  }
#+end_src


(setq org-latex-preview-appearance-options
      '(:foreground default
        :background default
        :zoom 5
        :scale 5
        :page-width 1.0))

(with-eval-after-load 'org
  (setq org-latex-preview-appearance-options
        (plist-put org-latex-preview-appearance-options :scale 3.8))
  (setq org-latex-preview-appearance-options
        (plist-put org-latex-preview-appearance-options :zoom 3.2)))


(setq ajlua2
      '(ajlua2
        :programs ("lualatex" "inkscape")
        :description "pdf > svg"
        :message "you need to install the programs:lualatex and inkscape."
        :image-input-type "pdf"
        :image-output-type "svg"

        ;; ⬅️ scale factor: (BUFFER . HTML)
        ;; try (1.7 . 1.7) or (2.0 . 2.0) for bigger previews
        :image-size-andjust (2.0 . 2.0)
        :image-size-adjust (1.0 . 1.0)	
        :post-clean ("")
        :latex-compiler
        ("lualatex -interaction=nonstopmode --shell-escape --output-directory=%o %F")
        :image-converter
        ("inkscape --pdf-poppler --export-text-to-path --export-plain-svg --export-area-drawing --export-filename=out.svg %f"
         "echo image converter was run >> /Users/aayushbajaj/Documents/site/content/projects/dl/perceptron/debug.tex"
         "inkscape --pdf-poppler --export-text-to-path --export-plain-svg --export-area-drawing --export-filename=%O %f")
        :transparent-image-converter
        ("inkscape --pdf-poppler --export-text-to-path --export-plain-svg --export-area-drawing --export-filename=%O %f")))

(add-to-list 'org-preview-latex-process-alist ajlua2)
(setq org-preview-latex-default-process 'ajlua2)

(with-eval-after-load 'org
  (setq org-format-latex-options
        (plist-put org-format-latex-options :scale 1.8)))

(setq org-format-latex-options (plist-put org-format-latex-options :scale 1.0))