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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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Triss [41]
We have to find the expected value for the PlayBall lottery. 
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Prize amount = $250
If a player wins, he will be winning $249 as the price is not paid back along with the prize amount. He is spending $1, getting back $250, so the net amount he is getting back is $249.

Now we have to find the probability of winning and losing.

Number of letters from A to T = 20
Number of digits from 0 to 9 = 10

Probability of picking up the same letter that was picked on that day = 1/20
Probability of picking up the same number that was picked on that day = 1/10

Thus, the Probability of picking up the same letter and same number that was picked on that day = \frac{1}{20}* \frac{1}{10}= \frac{1}{200}

Thus, the probability of winning = 1/200

The probability of losing = 1- \frac{1}{200}=\frac{199}{200}

The expected value E for the PlayBall lottery will be:

E= \frac{1}{200}(249)- \frac{199}{200}(1) \\  \\ 
E= \frac{1}{4}  \\  \\ 
E=0.25

Thus, the option C gives the correct answer
4 0
3 years ago
Solve the following proportion.<br> х<br> 42<br> 35<br> 10
anzhelika [568]

Answer:

12

Step-by-step explanation:

The proportion is equal to \frac{x}{10}=\frac{42}{35}

We can simplify the right side by dividing by 7/7 to get the right side equal to 6/5. Now we can cross-multiply to get

60=5x

Dividing both sides by 5, we have the answer as

x=12

6 0
2 years ago
A watermelon seed is 0.4 long. How far would a line of 112 watermelon seeds stretch?
Korvikt [17]

Since one watermelon seed is 0.4 long, you can multiply 0.4 by 112

0.4 x 112 = 44.8

So it will be 44.8 long

8 0
3 years ago
What is the value of the whole number n if: n=1/2 of 2/3 of 3/4 of 4/5 of 100
OverLord2011 [107]
20 I think it is 20 .................
3 0
3 years ago
Factor xy−4y+4x−16 by grouping
maksim [4K]

Answer:

(y+4)(x-4)

Step-by-step explanation:

Given the expression:

xy-4y+4x-16

(xy-4y)+(4x-16)

Take the common factor

y(x-4)+4(x-4)

(y+4)(x-4)

6 0
3 years ago
Read 2 more answers
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