Expected Value

I have stuck in a problem ........ Please help me....The problem is ............

A box contains 25 balls which are numbered from $1$ to $25$ . I took a ball.What is the expected number that the ball have?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

The answer is $13$ . [provided that all the balls have an equal chance of being selected]

The expected value of a random variable is the weighted average of all possible outcomes.

In your example the probability of a ball being selected is $\frac{1}{25}$ . So the expected value would be:

$1(\frac{1}{25})+2(\frac{1}{25})+3(\frac{1}{25})+4(\frac{1}{25})+\cdots + 23(\frac{1}{25})+ 24(\frac{1}{25})+25(\frac{1}{25})$

$=13$ .

Hope this helps!

Mursalin Habib - 7 years, 11 months ago

You might want to read this: Expected Value | Brilliant

Tim Vermeulen - 7 years, 11 months ago

Something's terribly wrong with your link. It redirects me to this page again.

You probably wanted to post this link.

Mursalin Habib - 7 years, 11 months ago

Thanks for pointing that out, I've updated it.

Tim Vermeulen - 7 years, 11 months ago

If I choose a ball again with out replace the first ball .What is the expected value of the second ball?

Kiriti Mukherjee - 7 years, 11 months ago

We are not here to solve problems for you. Mursalin H. told you how to solve the first problem, and if you understand it completely, you should be able to solve this one yourself. I have also provided you with the Brilliant post about the expected value, which will help you understand the concept.

Tim Vermeulen - 7 years, 11 months ago

Just call me Mursalin. Mursalin H. sounds really odd! :)

Mursalin Habib - 7 years, 11 months ago

wen all are equiprobable how can one of them(13) have more chances of appearing

Naga Teja - 7 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$