Probability and Statistics Calc Based

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Homework Statement


that it is exact...
[/B]
X and Y are discrete random variables with joint pmf

Chart attached
Capture.PNG



(a) Find V ar(X) and Var(Y).
(b) Find Cov(X; Y).
(c) Find the correlation of X and Y.
(d) Find the conditional distribution of X given that Y= 3

Homework Equations



Trying to check my answers to see if i am correct.


The Attempt at a Solution


[/B]
a. Var(x) = 0.8 Var(Y) = 1
b. 0.4
c. 0.1414
d. 1/5;1/5;3/5

Thanks
 
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Dr. Courtney said:
What is pmf?
probability mass function
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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