STAT333 Lecture 4: 333 Lecture 4
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2 gcxi pcx xi f gutted dx a properties of expectation. F xn is the nth moment of r v x. Elk e var sometimes denoted as e or e. Ely prov variance and covariance quadratic variance is is bilinear covariance translation invariant. If xiy then cocky 0 with varcxty valet bar. The converse is not true covariance is o d independence. E ely varcx t vara uncorrelated is enough always true only if. Need to remember that the first result and the other 2 results an different in nature. For a given i is also denoted as. Proof8 ria d p ewe i cw d. Tetxnbinen d x is trials in of n bernoulli success of successes each with probability p x when i. In indicators for independent events is success 01w ii. 0 hence ii distributed ar iid r v s independent identically. Eli pt to. at elin t p np var t varci varcid too.
