The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable takes on where the weighting is according to the relative frequency of occurrence of those individual values. For an absolutely continuous random variable it is the integral of values x multiple=iedmultiplied by the probability density. Observed data can be viewed as the values of a collection of independent identically distributed random variables. The sample mean )(or sample expectation) is defined as the expectation of the data with respect to the empirical distribution for the observed data. This makes it simply the arithmetic average of the data.
The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable takes on where the weighting is according to the relative frequency of occurrence of those individual values. For an absolutely continuous random variable it is the integral of values x multiple=ied by the probability density. Observed data can be viewed as the values of a collection of independent identically distributed random variables. The sample mean )or sample expectation) is defined as the expectation of the data with respect to the empirical distribution for the observed data. This makes it simply the arithmetic average of the data.
The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable takes on where the weighting is according to the relative frequency of occurrence of those individual values. For an absolutely continuous random variable it is the integral of values x multiplied by the probability density. Observed data can be viewed as the values of a collection of independent identically distributed random variables. The sample mean (or sample expectation) is defined as the expectation of the data with respect to the empirical distribution for the observed data. This makes it simply the arithmetic average of the data.
The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable takes on where the weighting is according to the relative frequency of occurrence of those individual values. For an absolutely continuous random variable it is the integral of values x multiple=ied by the probability density. Observed data can be viewed as the values of a collection of independent identically distributed random variables. The sample mean )or sample expectation) is defined as the expectation of the data with respect to the empirical distribution for the observed data. This makes it simply the arithmetic average of the data.