Review of Gaussian random variables If x is a Gaussian random
... independent random variables. Thus hyr ys yp yq i = hyr ys iδrs hyp yq iδpq + hyr yp iδrp hys yq iδsq + hyr yq iδrq hys yp iδsp (33) (which is true as a special case when r = s = p = q). Substituting this back into (32), we conclude that hxi xj xk xm i = hxi xj ihxk xm i + hxi xk ihxj xm i + hxi xm ...
... independent random variables. Thus hyr ys yp yq i = hyr ys iδrs hyp yq iδpq + hyr yp iδrp hys yq iδsq + hyr yq iδrq hys yp iδsp (33) (which is true as a special case when r = s = p = q). Substituting this back into (32), we conclude that hxi xj xk xm i = hxi xj ihxk xm i + hxi xk ihxj xm i + hxi xm ...
Mean, Variance, and Standard Deviation
... It is easy to show that the variance is simply the mean squared deviation from the mean. Covariance and Correlation Next, let (X1 , Y1), (X2 , Y2) ,…, (Xn , Yn) be n pairs of values of two random variables X and Y. We wish to measure the degree to which X and Y vary together, as opposed to being ind ...
... It is easy to show that the variance is simply the mean squared deviation from the mean. Covariance and Correlation Next, let (X1 , Y1), (X2 , Y2) ,…, (Xn , Yn) be n pairs of values of two random variables X and Y. We wish to measure the degree to which X and Y vary together, as opposed to being ind ...
Mean/expected value/expectation of a discrete random variable
... Let X be a discrete random variable defined on the probability space (S, C, P ). Its range (set of possible values) is countable. The mean or expected value or expectation of X, denoted E(X) (or sometimes just EX) or µX (or sometimes just µ), is defined by the sum E(X) := ...
... Let X be a discrete random variable defined on the probability space (S, C, P ). Its range (set of possible values) is countable. The mean or expected value or expectation of X, denoted E(X) (or sometimes just EX) or µX (or sometimes just µ), is defined by the sum E(X) := ...