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Statistics Homework Solutions 113

Statistics Homework Solutions 113 - 113 SUPPLEMENTARY...

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Unformatted text preview: 113 SUPPLEMENTARY EXERCISES FOR CHAPTER 4 (e) Yes. Almost none of the samples will have a total weight of 910.3 ounces or less if the claim is true. (f) Yes, because a total weight of 910.3 ounces is unusually small if the claim is true. e0 1 ¡¥ ln 2 1 e F0 e ¡ ¡¥ ¤ 0 21. (a) P X ¤ ¨ e ln2 12 e ¡¥ e xm ¡ 1 F ln 2 1 ¡ ¤ 1 ¡ ¡ ¡¥ ln 2 e PX ¦ ¤ ¨ ¡ ¡¥ ¡ (b) P X ¤ ¤ ¡ ¡ ¡ ¨ ¡ ¡ xαβ β ex β2 ¡¥ ¢ ¢ ¡¥¤ ¢ ¡¥¤ ¤ ¡¥ ¤ ¡ ¥¤ t PX s 1 ps ¥ ¡ ¡ ¥ ¤ £ ¥ ¤£ ¡ ¢ ¢ ¤ ¡ s ¥ ¢ ¡ ¥ ¤ ¥ ¡ ¤ ¡ ¥ ¡ ¡ ¢ ¡ ¤ ¡ ¤ ¡ ¤ ¡ ¡¥ ¡ ¤ ¡ Note that if X s t , it must be the case that X P X s t and X s PX s t. ¡ ¡ 1 pt PX t t s PX £ ¥ PX s 1 ps t and X ¤ s s ¡ PX p α. ¥ ¤ s ¡¥ tX ¤ s 1 ¡ (b) P X P First s trials are failures ¥ s ¡ ¦ ¢ β1 ¡ ¡ ex ¦ ¦ ¡ ¡ ¢ x α β2 (c) Since fX x is symmetric around α, its center of mass is at x 25. (a) P X 0 3665. ¦ x ln ln 2 ¡¥ e ln 2, so xm ¨ fX α ¤ x β1 ¡¥ (b) fX α e Fx 23. (a) fX x ln0 5 0 5. ¡ Solving for xm yields e xm e ¨ (c) Let xm be the median of X . Then F xm s, which is the reason that ¥ ¡ ¢ ¤ ¡ ¡¥ ¡ ¢ ¡ ¢ ¤ (c) Let X be the number of tosses of the penny needed to obtain the first head. PX ¡ ¤ ¡¥ 3 2 ¡¥ ¡ 5X 1 4. £ ¡ Then P X ¤ The probability that the nickel comes up tails twice is also 1/4. ...
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