Question

It is solved with the following function:
f(x) = A sin(n*π*x/L) Maximum
If the function is defined between zero and L, find where it is at a maximum. In terms of probability, what is this telling you physically?

Probability
For n = 4, write down (but do not solve) the integral you would need to evaluate to see if the object is between 0 and L/3. Please include a sketch.

Answer 1

1)
A sin L
for $0\le x\le L$

Then the maximum occurs for

nTT TT sin 1+ L

This means the object is most likely to be found at the middle

2) Sketch to explain the situation:

x-0 x L3

The set-up of the integral is:

f(x) dr A sin L dr

$\blacksquare$

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