Search results
Results from the WOW.Com Content Network
Here the independent variable is the dose and the dependent variable is the frequency/intensity of symptoms. Effect of temperature on pigmentation: In measuring the amount of color removed from beetroot samples at different temperatures, temperature is the independent variable and amount of pigment removed is the dependent variable.
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
Independent: Each outcome will not affect the other outcome (for from 1 to 10), which means the variables , …, are independent of each other. Identically distributed : Regardless of whether the coin is fair (with a probability of 1/2 for heads) or biased, as long as the same coin is used for each flip, the probability of getting heads remains ...
In that model, the random variables X 1, ..., X n are not independent, but they are conditionally independent given the value of p. In particular, if a large number of the X s are observed to be equal to 1, that would imply a high conditional probability , given that observation, that p is near 1, and thus a high conditional probability , given ...
Let be the product of two independent variables = each uniformly distributed on the interval [0,1], possibly the outcome of a copula transformation. As noted in "Lognormal Distributions" above, PDF convolution operations in the Log domain correspond to the product of sample values in the original domain.
Pairwise independent random variables with finite variance are uncorrelated. A pair of random variables X and Y are independent if and only if the random vector ( X , Y ) with joint cumulative distribution function (CDF) F X , Y ( x , y ) {\displaystyle F_{X,Y}(x,y)} satisfies
Further, two jointly normally distributed random variables are independent if they are uncorrelated, [4] although this does not hold for variables whose marginal distributions are normal and uncorrelated but whose joint distribution is not joint normal (see Normally distributed and uncorrelated does not imply independent).
Probability generating functions are particularly useful for dealing with functions of independent random variables. For example: For example: If X i , i = 1 , 2 , ⋯ , N {\displaystyle X_{i},i=1,2,\cdots ,N} is a sequence of independent (and not necessarily identically distributed) random variables that take on natural-number values, and