Find the Mean and Variance of Random Variable Z = (5x+3)

rogo0034
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Homework Statement


Find the Mean and Variance of Random Variable Z = (5x+3)

Using data set:
AwPGYl.jpg
Using:
eRRWt.png

&
8gkTw.png

The Attempt at a Solution

 
Last edited:
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Sorry the data set it so large, I've been trying to adjust it to no avail.EDIT: Fixed it, should be easier to view now
 
Last edited:
rogo0034 said:

Homework Statement


Find the Mean and Variance of Random Variable Z = (5x+3)

Using data set:
AwPGYl.jpg



Using:
eRRWt.png

&
8gkTw.png




The Attempt at a Solution


You have a very small table of x and f(x) values. What is stopping you from computing EX? Why don't you just compute EX, then use that value in the computation of Var(X) = sum f(x)*(x-EX)^2 ?

RGV
 
They want us to use the theorem and corollary, any ideas? I'm not too savvy with this stuff yet.
 
rogo0034 said:
They want us to use the theorem and corollary, any ideas? I'm not too savvy with this stuff yet.

OK, so use the theorem and the corollary. Does the first theorem have E(X) in it? Do you know the value of E(X)? If not, you need to compute it. Does the second theorem have \text{Var}(X) = \sigma_x^2 in it? Do you know the value of Var(X)? If not, you need to compute it.

RGV
 
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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