Calculations with Random Variables

I have a hard time understanding all the formulas without examples. a's and b's and f(x) is just confusing but if I have an example with real numbers plugged in I can understand.

Can anyone help me with
Please explain this to me...I have no idea how I can get an answer with 2 unknowns
find the numeric value of k
f(x)={(k/x for 1≤ x≤10
0 Otherwise


I believe x is going to be 10 as 1≤ x≤10. But from there I am lost.

medako said:

Please explain this to me...I have no idea how I can get an answer with 2 unknowns
find the numeric value of k f(x)={(k/x for 1≤ x≤10, 0 Otherwise.

Click to expand...

You have stated this poorly.
Is it a discrete RV or a continuous RV.

If discrete then \(\displaystyle x=1,2,\cdots,10\) then solve \(\displaystyle \displaystyle\sum\limits_{x = 1}^{10} {\frac{k}{x}} = 1\) for \(\displaystyle k\)

If continuous, that is \(\displaystyle x\in[1,10]\) then solve for \(\displaystyle k\) in \(\displaystyle \displaystyle\int_1^{10} {\frac{kdx}{x}} = 1\).

pka said:

You have stated this poorly.
Is it a discrete RV or a continuous RV.

If discrete then \(\displaystyle x=1,2,\cdots,10\) then solve \(\displaystyle \displaystyle\sum\limits_{x = 1}^{10} {\frac{k}{x}} = 1\) for \(\displaystyle k\)

If continuous, that is \(\displaystyle x\in[1,10]\) then solve for \(\displaystyle k\) in \(\displaystyle \displaystyle\int_1^{10} {kxdx} = 1\).

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Sorry I am so flustered I didn't even think about that. It is continuous. But I'm still not understanding what all the kxdx means

medako said:

Sorry I am so flustered I didn't even think about that. It is continuous. But I'm still not understanding what all the kxdx means

Click to expand...

I edited my reply it should be
\(\displaystyle \displaystyle\int_1^{10} {\frac{k}{x}dx} = 1\)