# Homework #7: Coin Flipping

**Due: May 16, 2016 at 14:00.**

*Read and understand the following instructions on submission of
homework.* **If you do not follow them, you will not receive credit.**

Write a *plain text* e-mail to me. This homework does contain special
symbols, but you can copy and paste them from the assignment if you
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the mail the subject "01CN101 Homework #4 by <your name>" in *hankaku
romaji* and send it to math-hw@turnbull.sk.tsukuba.ac.jp. (This
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Make sure that the body of the email contains your *name* and *student
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# Problems

## Problem 1

Suppose you conduct the experiment of flipping a coin 5 times, and
counting how many times of 5 "heads" and "tails" appear. Set the null
hypothesis H0 as "the coin is unbiased" (also called "fair"). Under
H0, compute the distributions of f(heads) and f(tails) ("f(X)" means
"count how many times X comes up"). Let P(type II error) = 20%, and
determine the critical regions for the one-tailed test and for the
two-tailed test of H0.

日本語版 は授業で話した内容で省略されたものなので英語版の方が正確
と考える。

**Due: May 16, 2016 at 14:00.**