# Thread:

1. ## Probability Distribution Function Help

Given the probability distribution function:

Determine the:
1. Probability density function.
2. The mean.
3. The median.
Hello,
I am really struggling with this subject area, this is an example I have found, would someone be able to go through a solution so I can begin to understand it a bit more.
Appreciate any help in advance.
Thanks.

2. Originally Posted by jscfc
Given the probability distribution function:

Determine the:
1. Probability density function.
2. The mean.
3. The median.
Hello,
I am really struggling with this subject area, this is an example I have found, would someone be able to go through a solution so I can begin to understand it a bit more.
Appreciate any help in advance.
Thanks.
First you have a typo in your problem.
Second we are not mind readers so please tell us that the function is the Cumulative distribution function
Cumulative distribution function - Wikipedia, the free encyclopedia

Your book or the above wiki will tell you that the CDF is the integral of the PDF

$\displaystyle F(X)=\int_{-\infty}^{x}f(t)dt$

So to undo an integral we will use the fundamental theorem of calculus to take the derivative of $F(x)$

This will give $f(x)$ the PDF

This will answer the rest of you question.

Exponential distribution - Wikipedia, the free encyclopedia

If you get stuck please post some work so we can see where.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8763407468795776, "perplexity_flag": "middle"}