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Question 2: Two jointly distributed continous random variables Let <KY < be two random variables jointly distributed with fxx(,y) -#(+"+rv): Answer the f...

Question

Question 2: Two jointly distributed continous random variables Let <KY < be two random variables jointly distributed with fxx(,y) -#(+"+rv): Answer the following questionsWhat the probability that 0.3<4 <0.7 and X z 0.75" What the marginal distribution of ? What is the marginal distribution of Y? What is PGX Y)? What is the the expxted value of and Y?Answer:

Question 2: Two jointly distributed continous random variables Let <KY < be two random variables jointly distributed with fxx(,y) -#(+"+rv): Answer the following questions What the probability that 0.3<4 <0.7 and X z 0.75" What the marginal distribution of ? What is the marginal distribution of Y? What is PGX Y)? What is the the expxted value of and Y? Answer:



Answers

Suppose that $X$ and $Y$ have the following joint probability distribution: \begin{tabular}{cc|cc}
& \multicolumn{2}{|c} {$x$} \\ \cline { 2 - 4 }$f(x, y)$ & 2 & 4 \\ \hline & 1 & 0.10 & 0.15 \\ $y$ & 3 & 0.20 & 0.30 \\ & 5 & 0.10 & 0.15 \end{tabular} (a) Find the marginal distribution of $X$. (b) Find the marginal distribution of $Y$.

You know there's probably been given the following probability distribution and I would like to find the marginal distributions not to find the marginal distribution for X. We need to integrate out the winds were entering out from 0 to 1. X plus Y. The wife. And so this gives us X. Y plus one half. Why squared evaluated from Y is 0- one. Mhm. And this is X plus one half. That's our marginal distribution threat. This acts plus 1/2 What? That's going from zero 20. Now for marginal distribution for what I notice that this is just going to be the exact same thing because you do the exact same mineral. So similarly we have F. Of why is why what? A half L&B. We want to find the probability that X is bigger than .25 and yeah why is greater than a half? Mhm. So here we need to integrate X. goes from 0 to 0.25. And why will then go from I'm sorry, extras from 0.25 to one. We have an upper amount of one. So it's 0.25-1. And why does from .5 to 1 about plus? Why the why? I'm sorry. Dx and Dy so integrating with respect to act first This is the integral from 0.5 to one of one half. Have squared plus. That's why evaluated from x 0.25- one. Do you want? Yeah. Uh huh. Yeah. So here's what we're going to do is plug in One party in 0.25 frets. That's attractive. And so this will have the interval from 0.5 to one Of .75. Y Plus .46875. Do you want? Now we integrate this and so this gives us, yeah, whenever we integrate .75 y plus .46875, we end up with 0.375 Y squared Plus .46875 Y, Evaluated from Y is 0.5- one. So then we plug in .5, we plug in one voice attractive. This is .5156- five.

Okay. So this is what's given notice that these numbers are all the same throughout the row. Uh This means that the variables are not associated, since we can't tell them apart, and with that we aren't able to determine what the marginal distributions are, So. Okay. Okay. Yeah. We don't know what the questions. We can't divide them by anything. And all we can tell you is that this is the distribution of the conditional distribution.


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