Continuous Random Variable: Difference between revisions
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The probability density function (pdf) maps a continuous variable to a | The probability density function (pdf) maps a continuous variable to a | ||
probability density. As the name "density" suggests, the area under the | probability density. As the name "density" suggests, the area under the | ||
pdf curve between a range is the probability of the variable being in | pdf curve between a range is the probability of the variable being in that range. | ||
<math> | |||
P(c \leq x \leq d) = \int_c^d f(x) dx = F(d) - F(c) | |||
</math> | |||
Total area under the curve must be <math> 1 </math>, as chances of | |||
events happening is 100% if the range includes all possible events. | |||
<math> | |||
\int_-\infty^\infty f(x) dx = 1 | |||
</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 07:29, 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
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.
Total area under the curve must be , as chances of
events happening is 100% if the range includes all possible events.
Uniform Distribution
is minimum, and
