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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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Is 5/3 a irrational number
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Step-by-step explanation: To determine whether 5/3 is rational or irrational, it's important to understand that all fractions positive or negative are rational numbers.

So 5/3 is not an irrational number, it's rational.

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A fenced in rectangular region with the dimensions 4 yards by 8 yards is suddenly expanded by the same distance in each dimensio
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The distance added to each dimension is 2 yards.

Step-by-step explanation:

The initial dimensions of the rectangular fence is 8 yards by 4 yards.

The initial area of the rectangular fence = area of a rectangle

area of a rectangle = length x width

So that,

The initial area of the fence = 8 x 4

                                              = 32

The initial area of the fence is 32 square yards.

But, with the new dimensions, area = 60 square yards.

(4 + x) x (8 + x) = 60

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x^{2} + 12x - 32 = 0

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3 years ago
The area of a rectangle is 5/6 sq foot. The width is 2/3 foot. The length of the rectangle is how many feet
max2010maxim [7]

Answer:

The answer is

\frac{5}{4}  \\

Step-by-step explanation:

Area of a rectangle = length × width

Since we are finding the length

<h3>length =  \frac{area}{width}  \\</h3>

From the question

area = 5/6 sq. feet

width = 2/3 foot

Substitute the values into the above formula and solve for the length

The length is

length =  \frac{5}{6}  \div  \frac{2}{3}  \\  =  \frac{5}{6}  \times  \frac{3}{2}  \\  =  \frac{5}{2}  \times  \frac{1}{2}  \\  =  \frac{5}{4}

We have the final answer as

\frac{5}{4}  \\

Hope this helps you

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1/6 of a minute.

Step-by-step explanation:

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