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Let X be uniform over (0, 1). Find E[X|X < 1 ].

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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