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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?

(a) Weibull, with ? = 2 and ? = $\sqrt{2?}$, (b) .542

Intro Stats / AP Statistics

Chapter 3

Continuous Random Variables and Probability Distributions

Section 9

Supplementary Exercises

Continuous Random Variables

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Okay, So we know that the horizontal and vertical areas from aiming at a point target are independent of each other and each have a normal distribution para meters. I mean off zero under standard deviation off one. Also, given that the density function F V is V over seating squared times E to the power monetary screwed over to signal skirt for one V is great in zero on, otherwise chicken to do so Basically for views. Liston culture. So no. Do we know that the standard norm alleviation distribution is? Trust me. Sure. She was one way consult be. I calculated the proportion of darts that land between 25 millimeters of the target. Okay, that's just given by the entry of 0 to 25. No FV TV. Did you go thio actual 0 25 of the over 20 squared. I am e to the minus fee squared over two times 20 squared TV. So if you succeed for V in terms of tea, get his tea. She was a negative V squared over two terms. 20 screamed, and we know the D key is therefore negative to v just differentiating Curator over two times 20 squared. This will then reduce this integral. You too. And to go who is you to 0.78 1 to 5 e to the power of negative Chief teach you. So if you're just playing the boundaries way, know that Did you bring this or just have the minus coming front? Something negative. Same boundaries. Oh, sure, which will give negative zero from 4578 plus one, which is equal to 0.542 which is the proportion of darts that land within 25 millimeters.

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