Continuous Random Variable: Difference between revisions
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\int_-\infty^\infty f(x) dx = 1 | \int_{-\infty}^\infty f(x) dx = 1 | ||
</math> | </math> | ||
= Uniform Distribution <math> X \sim Uniform(a, b) </math> = | = Uniform Distribution <math> X \sim Uniform(a, b) </math> = | ||
<math> a </math> is minimum, and <math> b </math> | <math> a </math> is minimum, and <math> b </math> | ||
Revision as of 07:30, 1 March 2024
Continuous random variables have an inifinite number of values for any given interval. While similar, the approach to analysis is very different from discrete variables
- Summation becomes integration
- Probability becomes area under a curve
Probability Distribution Function Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) }
The probability density function (pdf) maps a continuous variable to a probability density. As the name "density" suggests, the area under the pdf curve between a range is the probability of the variable being in that range.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P(c \leq x \leq d) = \int_c^d f(x) dx = F(d) - F(c) }
Total area under the curve must be Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 }
, as chances of
events happening is 100% if the range includes all possible events.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_{-\infty}^\infty f(x) dx = 1 }
Uniform Distribution Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X \sim Uniform(a, b) }
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a } is minimum, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b }
