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sergij07 [2.7K]
3 years ago
15

You have a ruler of length 1 and you choose a place to break it using a uniform probability distribution. Let random variable X

represent the length of the left piece of the ruler. X is distributed uniformly in [0, 1]. You take the left piece of the ruler and once again choose a place to break it using a uniform probability distribution. Let random variable Y be the length of the left piece from the second break. (a) Find the conditional expectation of Y given X, E(Y\X). (b) Find the unconditional expectation of Y. One way to do this is to apply the law of iterated expectation which states that E(Y) = E(E(Y\X)). The inner expectation is the conditional expectation computed above, which is a function of X. The outer expectation finds the expected value of this function. (c) Compute E(XY). This means that E(XY\X) = XE(Y\X) (d) Using the previous results, compute cov(X, Y).
Mathematics
1 answer:
salantis [7]3 years ago
6 0

Answer:

Step-by-step explanation:

idek

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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.
lora16 [44]
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.


The sum x^2+y^2 can be written as: x^2+y^2=(x+y)^2-2xy, 
<span>
from the binomial expansion formula: </span>(x+y)^2=x^2+2xy+y^2.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>

</span>x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x=10x^2-108x+18^2.

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.


At x=5.4, the expression 10x^2-108x+18^2, which is equivalent to x^2+y^2, takes it smallest value.

Substituting, we would find 10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324=32.4 This is the smallest value of the expression. 


For x=5.4, y=-3x+18=-3(5.4)+18=1.8.



Answer:   (5.4, 1.8)
8 0
3 years ago
Please help what is the answer a b c or d
bonufazy [111]

Answer:

A

Step-by-step explanation:

I did test rf

4 0
2 years ago
Ms. Monroe mixes 200 cubes of 4 different colors for a project. She then uses a scoop to place 20 cubes into each of 10 paper ba
Scilla [17]

Answer:

The mean no. of red cubes is more than the median no. of red cubes.

Step-by-step explanation:

According to the question, we can prepare the following table denoting the no. of bags containing any number of red cube(s). The no. of red cubes in each bag can theoretically be any no. between 0 and 20 (both end inclusive) as in total each bag contains 20 cubes of different colors.There are as a whole 10 bags (given).

No. of red cubes           No. of bags           (x_{i}f_{i})

 (x_{i})                                        (f_{i})

    0                                     2                             0

     1                                     0                             0

     2                                    2                             4

     3                                     1                             3

     4                                     1                             4

     5                                     0                            0

     6                                     1                              6

     7                                      2                           14

      8                                     1                             8

      9                                     0                            0

    10                                      0                            0

 Total                                 10                            39

Now, no. of bags containing no. of red cubes  above 10   is  0   [since there are as a whole 10 bags only]

       

So, from  the table we  get that  mean no, of red cubes in each bag

  = \frac {\sum_{i =1}^{10}x_{i}f_{i}}{\sum_{i=1}^{10}f_{i}}

  =  39/10 = 3.9

Also, from the table, we get that, no. of bags with no. of red cubes ≤ 3

= (2 + 2 + 1) = 5

and, no. of bags with no. of red cubes  ≥ 4

= (1 + 1 + 2 + 1) = 5

Also there are 1 bag each for no. of red cubes = 3 and 4

So. median no. of red cubes = (3 + 4)/2 = 3.5

So, we get that the mean no. of red cubes is more than the median no. of red cubes.

5 0
3 years ago
Read 2 more answers
My question is in the picture I tried to multiply -7 on both sides and got -147 I don't know if it's correct or if it's the righ
Mars2501 [29]

Answer:

-3

Step-by-step explanation:

-7b = 21

/ -7     / -7

b = -3

7 0
3 years ago
Read 2 more answers
Jordan places two boards end to end to make one shelf. The first board is 47-100 meter long.The second board is 5-10 meter long.
puteri [66]
The fraction 5/10 is the same as 50/100 because they are equivalent. It will take 10 group of 10 to get to the denominator 100, so it will take 10 groups of 5 in the numerator to make it equal.

The answer is 50/100.
4 0
3 years ago
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