the lady tasting tea pdf

《The Lady Tasting Tea》是一本由统计学家David Salsburg撰写的书籍，讲述了统计学的发展历史和基本原理。该书以一位品茶的女士为例，引出了统计学的概念与实践。

书中详细介绍了统计学的起源和发展，以及在不同领域中的应用。通过生动有趣的案例和故事，作者向读者解释了概率、推断、假设检验等统计学的重要概念，帮助读者更好地理解复杂的统计学理论。

通过《The Lady Tasting Tea》，读者可以了解到统计学在实际生活中的应用，例如医学研究、市场调查、环境监测等领域。作者还以简单易懂的语言解释了统计学的基本原理和方法，为统计学初学者提供了一本很好的入门书籍。

这本书的PDF版本可以帮助学生和研究者更方便地阅读和学习，同时也方便了教师在教学中引用相关内容。读者可以通过这本书更深入地了解统计学的重要性，以及如何应用统计学方法解决实际问题。

总的来说，《The Lady Tasting Tea》是一本既有趣又有教育意义的统计学著作，对于对统计学感兴趣的读者来说是一本值得阅读的书籍。

相关问题

Once upon a time, Toma found himself in a binary cafe. It is a very popular and unusual place. The cafe offers visitors k different delicious desserts. The desserts are numbered from 0 to k−1 . The cost of the i -th dessert is 2i coins, because it is a binary cafe! Toma is willing to spend no more than n coins on tasting desserts. At the same time, he is not interested in buying any dessert more than once, because one is enough to evaluate the taste. In how many different ways can he buy several desserts (possibly zero) for tasting? Input The first line of the input contains a single integer t (1≤t≤1000 ) — the number of test cases. Then follows t lines, each of which describes one test case. Each test case is given on a single line and consists of two integers n and k (1≤n,k≤109 ) — the number of coins Toma is willing to spend and the number of desserts in the binary cafe. Output Output t integers, the i -th of which should be equal to the answer for the i -th test case — the number of ways to buy desserts for tasting.

This is a classic problem of finding the number of subsets of a given set with a certain property. In this case, we want to find the number of subsets of the set {0,1,2,...,k-1} such that the sum of the elements in the subset is less than or equal to n.

We can use dynamic programming to solve this problem efficiently. Let dp[i][j] be the number of ways to choose a subset of the first i elements of the set {0,1,2,...,k-1} such that the sum of the elements in the subset is exactly j. Then the answer to the problem is the sum of dp[k][0] to dp[k][n].

The base case is dp[0][0]=1, since there is exactly one way to choose an empty subset with sum zero. For each i from 1 to k, we can either choose the i-th element or not. If we choose it, then we need to find the number of ways to choose a subset of the first i-1 elements with sum j-2i. If we do not choose it, then we need to find the number of ways to choose a subset of the first i-1 elements with sum j. Therefore,

dp[i][j] = dp[i-1][j] + dp[i-1][j-2i], if j>=2i
dp[i][j] = dp[i-1][j], otherwise

The final answer is the sum of dp[k][0] to dp[k][n]. The time complexity of this algorithm is O(kn).

Here is the Python code to solve the problem:

t = int(input())
for _ in range(t):
    n, k = map(int, input().split())
    dp = [[0] * (n+1) for _ in range(k+1)]
    dp[0][0] = 1
    for i in range(1, k+1):
        for j in range(n+1):
            dp[i][j] = dp[i-1][j]
            if j >= 2**i:
                dp[i][j] += dp[i-1][j-2**i]
    print(sum(dp[k]))

I hope this helps! Let me know if you have any more questions.

Once upon a time, Toma found himself in a binary cafe. It is a very popular and unusual place. The cafe offers visitors k different delicious desserts. The desserts are numbered from 0 to k−1. The cost of the i-th dessert is 2i coins, because it is a binary cafe! Toma is willing to spend no more than n coins on tasting desserts. At the same time, he is not interested in buying any dessert more than once, because one is enough to evaluate the taste. In how many different ways can he buy several desserts (possibly zero) for tasting? Input The first line of the input contains a single integer t (1≤t≤1000) — the number of test cases. Then follows t lines, each of which describes one test case. Each test case is given on a single line and consists of two integers n and k (1≤n,k≤109) — the number of coins Toma is willing to spend and the number of desserts in the binary cafe. Output Output t integers, the i-th of which should be equal to the answer for the i-th test case — the number of ways to buy desserts for tasting.用c++实现

算法：贪心

思路：

- 根据题目中的描述，可以得知每个点心的价格都是2的幂次方，因此可以从最便宜的点心开始购买，直到购买的点心总价格超过了n，或者购买的点心数量达到了k。
- 购买点心的过程中，可以使用一个变量sum记录购买的点心的总价格，另一个变量cnt记录购买的点心数量。

时间复杂度：$O(\log n)$

C++ 代码：