Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the possible values of x? O No. The expected value will never be one of its possible values of x. O Yes. The expected value must always be one of its possible values of x. O No. The expected value can be a value different from the exact value of x. O Yes. The expected value can never be a value from the exact value of x. Explain or give an example.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Question:**

Consider the probability distribution of a random variable \( x \). Is the expected value of the distribution necessarily one of the possible values of \( x \)?

- \( \bigcirc \) No. The expected value will never be one of its possible values of \( x \).

- \( \bigcirc \) Yes. The expected value must always be one of its possible values of \( x \).

- \( \bigcirc \) No. The expected value can be a value different from the exact value of \( x \).

- \( \bigcirc \) Yes. The expected value can never be a value from the exact value of \( x \).

**Prompt:**

Explain or give an example.

[Text box for input]
Transcribed Image Text:**Question:** Consider the probability distribution of a random variable \( x \). Is the expected value of the distribution necessarily one of the possible values of \( x \)? - \( \bigcirc \) No. The expected value will never be one of its possible values of \( x \). - \( \bigcirc \) Yes. The expected value must always be one of its possible values of \( x \). - \( \bigcirc \) No. The expected value can be a value different from the exact value of \( x \). - \( \bigcirc \) Yes. The expected value can never be a value from the exact value of \( x \). **Prompt:** Explain or give an example. [Text box for input]
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