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Sagot :
Using the uniform distribution, it is found that E[X|X < 1 ] = 0.5.
What is the uniform probability distribution?
It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The expected value is given by:
[tex]E(X) = \frac{a + b}{2}[/tex]
In this problem:
- The distribution is uniform over the interval (0, 1) hence [tex]a = 0,b = 1[/tex].
- We want the expected value considering X is less than 1, hence the value of bound b is still 1.
Then:
[tex]E(X|X < 1) = \frac{0 + 1}{2} = 0.5[/tex]
You can learn more about the uniform distribution at https://brainly.com/question/13889040
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