X1, X2, X3 on a spnning fair wheel three times

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In summary, the probability of getting X1, X2, or X3 on a spinning fair wheel three times is 1/3 or approximately 33.33%. There are 27 total outcomes possible when spinning a fair wheel three times. The probability of getting the same outcome three times in a row on a spinning fair wheel is 1/27 or approximately 3.70%. There is no way to increase the chances of getting X1, X2, or X3 on a spinning fair wheel three times, and the outcomes cannot be predicted due to the principle of probability.
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robert5
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Three random variables are generated X1, X2, X3 on a spnning fair wheel three times. these variables are independent and uniformaly distributes on [0,1]. find probability that these values are none within +-d of each other where 0<=Y1<=Y2<=Y3<=1 is order statistics for randon variables.
fY2Y3(y2,y3) = 2!fx(y) . fX(y) =

what is fX(y)? can some one help?

Also,

Pr[d<=Y2<=(1.2d), (y2+d)<=Y3<=(1-d)] =

where y2 and y3 be placed in [0, 1]

I can understand it but don't know how to do it...
 
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order statistics

any one helping ...
 

Related to X1, X2, X3 on a spnning fair wheel three times

1. What is the probability of getting X1, X2, or X3 on a spinning fair wheel three times?

The probability of getting X1, X2, or X3 on a spinning fair wheel is 1/3 or approximately 33.33%. This is because there are three possible outcomes (X1, X2, or X3) out of a total of three spins. Each outcome has an equal chance of occurring, making the probability 1/3.

2. How many total outcomes are possible when spinning a fair wheel three times?

There are 27 total outcomes possible when spinning a fair wheel three times. This is because each spin has three possible outcomes (X1, X2, or X3), and when you spin three times, the total number of outcomes is calculated by multiplying 3 by itself three times (3 x 3 x 3 = 27).

3. What is the probability of getting the same outcome three times in a row on a spinning fair wheel?

The probability of getting the same outcome (X1, X2, or X3) three times in a row on a spinning fair wheel is 1/27 or approximately 3.70%. This is because the probability of getting the same outcome on each spin is 1/3, and to calculate the probability of three independent events occurring in a row, you multiply the probabilities together (1/3 x 1/3 x 1/3 = 1/27).

4. Is there a way to increase the chances of getting X1, X2, or X3 on a spinning fair wheel three times?

No, there is no way to increase the chances of getting X1, X2, or X3 on a spinning fair wheel three times. Each spin is independent and has an equal chance of occurring, regardless of previous outcomes. This is the principle of probability and it applies to spinning fair wheels as well.

5. Can the outcomes of spinning a fair wheel three times be predicted?

No, the outcomes of spinning a fair wheel three times cannot be predicted. As mentioned before, each spin is independent and has an equal chance of occurring. Therefore, it is impossible to predict the exact outcome of each spin. However, we can calculate the probability of certain outcomes occurring based on the number of possible outcomes and the number of desired outcomes.

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