How Does Shooter Accuracy Affect Probability of Hitting a Target?

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Homework Help Overview

The discussion revolves around a problem involving a rifle shooter aiming at a target, where the shooter's accuracy is described by a probability density function. The original poster seeks to calculate the probability density for where the bullet strikes the target and how this relates to the width of the target and the angle of accuracy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the angle of accuracy and the resulting probability density function for where the bullet strikes. Questions arise regarding the definitions of variables such as D, d, and the angles involved. Some participants attempt to clarify the integration process for calculating probabilities from the probability density function.

Discussion Status

The discussion is active, with participants providing insights and asking clarifying questions. There is an ongoing exploration of the definitions and relationships between the variables involved, as well as attempts to derive expressions for the probability density function. Some participants express confusion about the notation and the implications of different angles.

Contextual Notes

Participants note the importance of understanding the context of the problem, including the implications of the probability density function and the assumptions about the angles involved. There is a mention of the need to clarify the roles of different symbols and the potential for confusion when transferring concepts from different contexts.

  • #31
Looks right to me.
So now, what about P(H;Φ)? Hint: there's an easier way than using p(x).
 
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  • #32
is it 1 when, theta is greater than Phi?
 
  • #33
is it 1 when, theta is greater than Phi?
... when the target area is bigger than the spread of the bullets? Well... yes. That would be part of the answer.

You are thinking along the right lines though...
How about when ##\theta < \Phi##?
How would you determine the probability that ##\phi## is inside a certain angle?
 

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