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eimsori [14]
3 years ago
7

For this problem, prove/derive the formula that allows one to find an expected value for X by conditioning on Y :

Mathematics
1 answer:
zimovet [89]3 years ago
6 0

Answer:

E[X |Y=y] = \int_{-\infty}^{\infty} x f_{X,Y} (x|y) dx

E[X|Y=y] =\sum_{x} x f_{X,Y} (x|y)

Step-by-step explanation:

For this case we assume that we have two random variable X and Y continuous, and we define the conditional density of X given Y like this:

f_{X|Y} (x|y) = \frac{f_{X,Y} (x,y)}{f_Y (y)}

Where f_{X,Y} (x,y) is the joint density function. And we can define the conditional probability like this:

P(a\leq X \leq b | Y = y) = \int_{a}^b f_{X,Y} (x|y) dx

In order to find the expected value of X given Y=y we just need to find this:

E[X | Y=y] = \int_{-\infty}^{\infty} x f_{X,Y} (x|y) dx

And if we assume that the random variable is discrete then the conditional expectation would be given by:

E[X|Y=y] =\sum_{x} x f_{X,Y} (x|y)

And as we can se just change the integral by a sum over the values defined for X, and with this we have the general formulas in order to find the conditional expectation of X given Y=y for the possible cases for a random variable.  

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Angelina_Jolie [31]
The string is assumed to be massless so the tension is the sting above the 12.0 N block has the same magnitude to the horizontal tension pulling to the right of the 20.0 N block. Thus, 
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2.04 a = T - 20.0 x 0.325 (using µ(k) for the coefficient of friction) 
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[eqn 1] + [eqn 2] → 3.26 a = 5.5 
a = 1.69 m/s² 


Subs a = 1.69 into [eqn 2] → 2.04 x 1.69 = T - 6.5 
T = 9.95 N 

Now want the resultant force acting on the 20.0 N block: 
Resultant force acting on the 20.0 N block = 9.95 - 20.0 x 0.325 = 3.45 N 
<span>Units have to be consistent ... so have to convert 75.0 cm to m: </span>

75.0 cm = 75.0 cm x [1 m / 100 cm] = 0.750 m 
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3 years ago
To multiply a decimal number by 100,
aleksley [76]

Answer:

move the decimal point two points to the right

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3 years ago
I need help with this .
vaieri [72.5K]
I would be glad to help you! I will solve through 3 to get you started.

This is a very important concept, so it would be helpful if you learn it on your own.

C= 2* pi* r

1. The radius is 5 cm. 5 cm represents r in the equation.
C= 2* 3.14 (or pi)* 5 
Multiply it by using a calculator. 
My answer was 31.4.

Let's try the second one.
2. The diameter is 9. Have of the diameter is the radius. 
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C= 2*3.14*4.5
I got 28.26

One more. 
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Make sure to add the end signs to you answer, ft, cm, meter, etc.

Let me know if you need more help.

Brainliest answer is always appreciated.
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3 years ago
Evaluate and simplify <br><br> F(x)=3-6x^2 for f(x+3)
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Insert x + 3 instead of x into the equation of the function f(x):

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f(x + 3) = 3 - 6(x + 3)²

use (a + b)² = a² + 2ab + b²

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combine like terms

= -6x² - 36x - 51

<h3>Answer: f(x + 3) = -6x² - 36x - 51</h3>
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4 years ago
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