## How To Convert PDF Online?

## Easy-to-use PDF software

## Why can't we directly find the PDF of the transformation of random variables, say g(X) from the random variable X. Why do we have to first convert PDF into CDF and then have to differentiate to get to the PDF of the transformed random variable?

CDF stands for cumulative distribution function. It takes as input any real number, and returns as output a number from 0 up to 1. It is defined as \text{cdf}_X(a) = F_X(a) = \mathbb{P}(X \leq a). PDF stands for probability density function. It is a bit trickier to define. When X is a continuous random variable, then \text{pdf}_X(a) = f_X(x) = [\cdf_X(a)]' = d\text{cdf}_X(a)/da. When X is a discrete random variable, then \text{pdf}_X(a) = \mathbb(P)(X = a). So a CDF is a function whose output is a probability. The PDF is a function whose output is a nonnegative number. The PDF itself is not a probability (unlike the CDF), but it can be used to calculate probabilities. When X is a continuous random variable, then we use integration to calculate probabilities using the PDF. \mathbb{P}(X \in A) = \int_{a \in A} f_X(a) \ dx. When X is a discrete random variable, then we use summation to calculate probabilities using the PDF. \mathbb{P}(X \in A) = \sum_{a \in A} f_X(a).

PDF documents can be cumbersome to edit, especially when you need to change the text or sign a form. However, working with PDFs is made beyond-easy and highly productive with the right tool.

## How to Convert PDF with minimal effort on your side:

- Add the document you want to edit — choose any convenient way to do so.
- Type, replace, or delete text anywhere in your PDF.
- Improve your text’s clarity by annotating it: add sticky notes, comments, or text blogs; black out or highlight the text.
- Add fillable fields (name, date, signature, formulas, etc.) to collect information or signatures from the receiving parties quickly.
- Assign each field to a specific recipient and set the filling order as you Convert PDF.
- Prevent third parties from claiming credit for your document by adding a watermark.
- Password-protect your PDF with sensitive information.
- Notarize documents online or submit your reports.
- Save the completed document in any format you need.

The solution offers a vast space for experiments. Give it a try now and see for yourself. Convert PDF with ease and take advantage of the whole suite of editing features.

## Convert PDF: All You Need to Know

Begin{document} \label{simple.pdf} \math bf{CDF} \math bf{CDF}(x) = \int_a2f{(X_a)}. \end{document} \label{simple.pdf} \math bf{PDF} \math bf{PDF}(x) = \int_a2f({\Cdf_x}). \end{document} \begin{math par{1}\begin{array}{ll}x \LEQ 1 &\text{if} x > 1 \\ 1 \LEQ 2 &\text{if} x