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October 13th, 2017, 03:33 AM   #1
ZMD
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Expected Value of Discrete Random Variable

Suppose A and B are discrete random variables.
They have mean 0 and variance 1.
Let C =max(A$^2$,B$^2$)

Find:
1. E[Z] $\leq$ 2
2. p=cov(A,B). Prove that E[Z] $\leq$ 1-$\sqrt{1-p^2}$

I've done part 1, need help for part 2.

Last edited by ZMD; October 13th, 2017 at 03:36 AM.
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October 13th, 2017, 01:52 PM   #2
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I answered this in your other post. p=0 leads to impossible result.
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October 13th, 2017, 02:00 PM   #3
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Quote:
Originally Posted by mathman View Post
I answered this in your other post. p=0 leads to impossible result.
The Z is actually a C. My mistake.
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October 17th, 2017, 10:38 AM   #4
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by "discrete" do you mean "distinct"?

I don't see any reason the problem would be different using continuous vs. discrete random variables. The definition of covariance is slightly different but that wouldn't affect the problem any.

1) makes no sense, do you just want to find $E[C]$ ? Maybe it's less than or equal to 2, maybe it's not. We can determine this but the statement you've written makes no sense.

Additionally for (1) do we assume the two rvs are independent? That they have covariance $p$ ? If the latter how is (1) different than (2)? Even if the former, we would just substitute $0$ in for $p$

Could you make this question a bit more clear please?
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