- #1
zeeshahmad
- 27
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Homework Statement
A rifle shooter aims at a target, at a distance d, but has an accuracy controlled by a probability density:
[itex]\rho(\phi)=\frac{1}{2\Phi}[/itex]
[itex]\phi\in(-\Phi,\Phi)[/itex]
[itex]\phi\in(-\Phi,\Phi)[/itex]
where [itex]\phi[/itex] is the angle achieved and is bounded by the small angle [itex]\Phi[/itex].
(Refer to attachment for diagram)
Calculate the probability density for where the bullet strikes the target, [itex]\tilde{p}(x)[/itex]. (I've done this.. I think)
If a target is set up with a width of 2d, with success H say, being hitting the target and failure M say, being missed the target, calculate and depict the probability of hitting,
[itex]P(H;\Phi)[/itex]
as a function of [itex]\Phi[/itex] for fixed d and D with [itex]D=tan(\theta)[/itex]
Hint: Be careful about when [itex]\Phi=\phi[/itex]
Homework Equations
[itex]p(a,b)=\int{dx p(x)}[/itex]
The Attempt at a Solution
For the bit I've done,
I got [itex]\tilde{p}(x)=\frac{2\Phi}{\pi}[/itex]
I don't know where to start on the next bit, could someone give me a hint please?