Neel Faucher: Numerade Educator Profile

Probability with Applications in Engineering, Science, and Technology

Based on data from a dart-throwing experiment, the article "Shooting Darts" (Chance, Summer $1997 : 16-19$ proposed that the horizontal and vertical errors from aiming at a point target should be independent of each other, each with a normal distribution having mean 0 and standard deviation $\sigma .$ It can then be shown that the pdf of the distance $V$ from the target to the landing point is
$$f(v)=\frac{v}{\sigma^{2}} \cdot e^{-v^{2} /\left(2 \sigma^{2}\right)} \quad v>0$$
(a) This pdf is a member of what family introduced in this chapter?
(b) If $\sigma=20 \mathrm{mm}$ (close to the value suggested in the paper), what is the probability that a dart will land within 25 $\mathrm{mm}$ (roughly 1 in.) of the target?

Chapter 3: Continuous Random Variables and Probability Distributions

Section 9: Supplementary Exercises