## Go back to

.....The site is being constantly updated, so come back to check new updates.....

If you find any bug or need any improvements in solution report it here

# CDF to PDF Calculator

CDF is Cumulative distribution function. PDF is Probability density function. For converting CDF to PDF we must differentiate CDF. This CDF to PDF calculator is for continuous random variables.

INSTRUCTION: If you click on step function input box. A keyboard will appear. Use that keyboard to enter your function

Step functions Upper and lower limit of step function

## You can see a sample solution below. Enter your data to get the solution for your question

$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Green}{Function\;you\;entered\;is,\;}} \mathbf{\color{Red}{F(x)}} =\left\{\begin{matrix} \mathbf{\color{Red}{0}} & -\infty <x< 0.0 \\ \\ \mathbf{\color{Red}{\frac{x^{2}}{2}}} & 0.0 ≤x≤ 1.0 \\ \\ \mathbf{\color{Red}{\left(- \frac{x^{2}}{2} + 2 x\right) - 1}} & 1.0 ≤x≤ 2.0 \\ \\ \mathbf{\color{Red}{1}} & 2.0 <x< \infty \\ \\ \end{matrix}\right. \\ \\ \mathbf{\color{Green}{Now\;we\;have\;to\;find\;the\;derivative\;of\;each\;step\;function}} }$$
$$\displaylines{\operatorname{f_{1}}{\left(x \right)} \;=\; \frac{\mathrm{d}(F_{1}(x))\;}{\mathrm{d}x} = \frac{\mathrm{d}(0)\;}{\mathrm{d}x} \\ \\ \Rightarrow \mathbf{\color{Red}{0}} \\ \\ \operatorname{f_{2}}{\left(x \right)} \;=\; \frac{\mathrm{d}(F_{2}(x))\;}{\mathrm{d}x} = \frac{\mathrm{d}(\frac{x^{2}}{2})\;}{\mathrm{d}x} \\ \\ \Rightarrow \mathbf{\color{Red}{x}} \\ \\ \operatorname{f_{3}}{\left(x \right)} \;=\; \frac{\mathrm{d}(F_{3}(x))\;}{\mathrm{d}x} = \frac{\mathrm{d}(\left(-\;\frac{x^{2}}{2}\;+\;2\;x\right)\;-\;1)\;}{\mathrm{d}x} \\ \\ \Rightarrow \mathbf{\color{Red}{2 - x}} \\ \\ \operatorname{f_{4}}{\left(x \right)} \;=\; \frac{\mathrm{d}(F_{4}(x))\;}{\mathrm{d}x} = \frac{\mathrm{d}(1)\;}{\mathrm{d}x} \\ \\ \Rightarrow \mathbf{\color{Red}{0}} \\ \\ \;\mathbf{\color{Green}{The\;required\;PDF\;is\;}} \mathbf{\color{Red}{f(x)}} =\left\{\begin{matrix} \mathbf{\color{Red}{\operatorname{f_{1}}{\left(x \right)}}} & -\infty <x< 0.0 \\ \\ \mathbf{\color{Red}{\operatorname{f_{2}}{\left(x \right)}}} & 0.0 ≤x≤ 1.0 \\ \\ \mathbf{\color{Red}{\operatorname{f_{3}}{\left(x \right)}}} & 1.0 ≤x≤ 2.0 \\ \\ \mathbf{\color{Red}{\operatorname{f_{4}}{\left(x \right)}}} & 2.0 <x< \infty \\ \\ \end{matrix}\right. \\ \\ \;\mathbf{\color{Green}{That\;is\;}} \mathbf{\color{Red}{f(x)}} =\left\{\begin{matrix} \mathbf{\color{Red}{0}} & -\infty <x< 0.0 \\ \\ \mathbf{\color{Red}{x}} & 0.0 ≤x≤ 1.0 \\ \\ \mathbf{\color{Red}{2 - x}} & 1.0 ≤x≤ 2.0 \\ \\ \mathbf{\color{Red}{0}} & 2.0 <x< \infty \\ \\ \end{matrix}\right. \\ \\ }$$