bet X and Xe be two random variable such that the Condiional distribuhons and means exist. Show thak a. E(xit XelXz) = E(xi\x2) +Xz
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Here's the explanation is as follows;
Part a)
First we need check the identities conditioning on X2 = x2 : that is ,
E(X1+X2 / X2 = x2 ) = E(X1 / X2 = x2) + E(X2 / X2 = x2 ).
= E(X1 / X2 = x2) + x2.
It follows from linearity of expectations.
The fact that X1 and X2 are constants when condition on X2 = x2 , the identity holds for every possibility of x2 on sample space.
Therefore , the equation holds for the random variable X2.
Thus , E(X1+X2 / X2) = E(X1 / X2) + X2.
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