# Aspects of bounded integral operators in Lp spaces by G.O. Okikiolu

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By G.O. Okikiolu

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This summation process is called marginalizing over y or integrating out the variable y. Of course, we can also determine the probability of y by marginalizing over x. These notions of conjoint and marginal probabilities also apply to beliefs. Consider, for example, two coins: a nickel and a dime. Suppose that we believe that they might be fair, or that they are trick coins with heads on both sides or with tails on both sides. We believe most strongly that they are both fair, but that there is a small chance that they are trick coins.

1 Discrete distributions: Probability mass . . . . . 2 Continuous distributions: Rendezvous with density† . 1 Properties of probability density functions . 2 The normal probability density function . . 3 Mean and variance of a distribution . . . . . . 1 Mean as minimized variance . . . . . 4 Variance as uncertainty in beliefs . . . . . . 5 Highest density interval (HDI) . . . . . . . Two-way distributions . . . . . . . . . . . 1 Marginal probability .

For example, the sample space of a flipped coin has two discrete outcomes, and we talk about the probability of head or tail. The sample space of a six-sided die has six discrete outcomes, and we talk about the probability of 1 dot, 2 dots, and so forth. ” For example, although calories consumed in a day is a continuous scale, we can divide up the scale into a finite number of intervals, such as <1500, 1500-2000, 2000-2500, 2500-3000, and >3000. Then we can talk about the probability of any one of those five intervals occurring: The probability of 2000-2500 is perhaps highest, with the probabilities of the other intervals dropping off from that high.