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Looks right to me.
So now, what about P(H;Φ)? Hint: there's an easier way than using p(x).
So now, what about P(H;Φ)? Hint: there's an easier way than using p(x).
How Does Shooter Accuracy Affect Probability of Hitting a Target?
- Thread starter zeeshahmad
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SUMMARY
The discussion focuses on calculating the probability density function for a rifle shooter's accuracy, defined by the angle error density function ρ(φ) = 1/(2Φ) for φ in (-Φ, Φ). The participants derive the probability density for where the bullet strikes the target, denoted as 𝑝(𝑥) = 1/π * (D/(D²+x²)), and confirm that 𝜏(𝑥) = 2Φ/π is the correct expression for the probability density function. Key variables include D (distance to the target), d (radius of the target), and θ (angle of error). The conversation emphasizes the importance of correctly interpreting the relationships between these variables.
PREREQUISITES- Understanding of probability density functions and integration.
- Familiarity with trigonometric functions, particularly tangent and arctangent.
- Knowledge of basic statistics, including uniform distributions.
- Ability to manipulate and differentiate mathematical expressions.
- Study the derivation of probability density functions in the context of angular errors.
- Learn about the implications of uniform distributions in statistical mechanics.
- Explore the relationship between angle errors and distance errors in projectile motion.
- Investigate the use of arctangent in calculating probabilities related to angular measurements.
Students and professionals in physics, statistics, and engineering, particularly those involved in ballistics, projectile motion analysis, and accuracy optimization in shooting sports.
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