Blog: The probability density for an electron that has passed through an experimental apparatus is shown in the figure. If 4100 electrons pass through...

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First we determine the probability $\displaystyle{p}$ of the event that one electron will land in a specified strip. Then the expected number of such electrons will be $\displaystyle{p}\cdot{N},$ where $\displaystyle{N}$ is the total number of electrons.

By the definition of a probability density $\displaystyle{P}{\left({x}\right)},$ the probability of being between $\displaystyle{a}$ and $\displaystyle{b}$ is equal to $\displaystyle{\int_{{a}}^{{b}}}{P}{\left({x}\right)}{\left.{d}{x}\right.}.$ Here $\displaystyle{a}=-{0.1}$ mm and $\displaystyle{b}={0.1}$ mm. Because the given density is an even function, $\displaystyle{p}=\ldots$

Hello!

It is simple to write a formula for $\displaystyle{P}{\left({x}\right)}$ for $\displaystyle{x}$ between 0 and 3, it is $\displaystyle{P}{\left({x}\right)}=\frac{{1}}{{3}}-\frac{{x}}{{9}}$ (a straight line). Therefore

$\displaystyle{p}={2}{\int_{{0}}^{{0.1}}}{\left(\frac{{1}}{{3}}-\frac{{x}}{{9}}\right)}{\left.{d}{x}\right.}={2}{\left(\frac{{x}}{{3}}-\frac{{{x}}^{{2}}}{{18}}\right)}{{\mid}_{{{x}={0}}}^{{0.1}}}={2}\cdot{\left(\frac{{0.1}}{{3}}-\frac{{0.01}}{{18}}\right)}\approx{0.0656}.$

And the expected number is about $\displaystyle{4100}\cdot{0.0328}\approx{269}.$ This number is dimensionless.

Note that this number is the most probable, but the neighboring numbers are also very probable.

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The probability density for an electron that has passed through an experimental apparatus is shown in the figure. If 4100 electrons pass through...

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The probability density for an electron that has passed through an experimental apparatus is shown in the figure. If 4100 electrons pass through...

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What are the problems with Uganda&#39;s government?

What are the problems with Uganda's government?