#REDIRECT Continuous random variable
By one convention, a random variable ''X'' is called continuous if its cumulative distribution function is continuous. That is equivalent to saying that Pr[''X'' = ''a''] = 0 for all real numbers ''a'', i.e.: the probability that ''X'' attains the value ''a'' is zero, for any number ''a''. While for a discrete random variable one could say that an event with probability zero is impossible, this can not be said in the case of a continuous random variable, because then no value would be possible. This paradox is solved by realizing that the probability that ''X'' attains a value in an uncountable set (for example an interval (mathematics)) can not be found by adding the probabilities for individual values. By another convention, the term "continuous random variable" is reserved for random variables that have probability density functions. A random variable with the Cantor distribution is continuous according to the first convention, and according to the second, is neither continuous nor discrete nor a weighted average of continuous and discrete random variables. In practical applications random variables are often either discrete or continuous. Probability theory
I moved this from the main page: :A random variable is ''continuous'' if the set of all possible values it can assume forms an interval (mathematics), either finite or infinite. :The probability that a continuous random variable will take a value in any particular sub-interval is given by the probability density function. Not every variable whose range is an interval (surely of positive length?) has a probability density function. Are continuous random variables those whose cdf if continuous? user:AxelBoldt
See other meanings of words starting from letter:
Words begining with Continuous_random_variable:
Continuous_Random_Variable
Continuous_random_variable
Continuous_random_variable
Continuous Random Variable
#REDIRECT Continuous random variable
Continuous random variable
By one convention, a random variable ''X'' is called continuous if its cumulative distribution function is continuous. That is equivalent to saying that Pr[''X'' = ''a''] = 0 for all real numbers ''a'', i.e.: the probability that ''X'' attains the value ''a'' is zero, for any number ''a''. While for a discrete random variable one could say that an event with probability zero is impossible, this can not be said in the case of a continuous random variable, because then no value would be possible. This paradox is solved by realizing that the probability that ''X'' attains a value in an uncountable set (for example an interval (mathematics)) can not be found by adding the probabilities for individual values. By another convention, the term "continuous random variable" is reserved for random variables that have probability density functions. A random variable with the Cantor distribution is continuous according to the first convention, and according to the second, is neither continuous nor discrete nor a weighted average of continuous and discrete random variables. In practical applications random variables are often either discrete or continuous. Probability theory
Continuous random variable
I moved this from the main page: :A random variable is ''continuous'' if the set of all possible values it can assume forms an interval (mathematics), either finite or infinite. :The probability that a continuous random variable will take a value in any particular sub-interval is given by the probability density function. Not every variable whose range is an interval (surely of positive length?) has a probability density function. Are continuous random variables those whose cdf if continuous? user:AxelBoldt
See other meanings of words starting from letter:
C
CA | CB | CD | CE | CF | CG | CH | CI | CJ | CK | CL | CM | CN | CO | CP | CR | CS | CT | CU | CW | CX | CY | CZ |Words begining with Continuous_random_variable:
Continuous_Random_Variable
Continuous_random_variable
Continuous_random_variable
Sponsored links: praca, nurkowanie.
These materials are based on Wikipedia and licensed under the GNU FDL
YouTube.com videos better site than Turbo Tax 2007
