## 统计代写|统计计算代写Statistical calculation代考|The binomial distribution

Many investigations result in responses for which there are only two possible outcomes, such as yes or no, accept or decline, pass or fail, male or female, etc. These investigations are known as binomial investigations.

The binomial distribution describes the probability distribution resulting from the outcome of a binomial investigation. A binomial investigation usually involves repeating the basic investigation a fixed number of times $(n)$, called trials, and observing the number of times that the outcome of interest (success) $(x)$ occurs.

A binomial probability distribution allows us to calculate the probability of a specific number of successes $(x=0,1,2, \ldots, n) x$ times in a certain number of trials $(n)$
A binomial experiment has the following properties:

• The experiment must consist of $n$ identical trials.
• The trials are independent. That is, the outcome of one trial does not affect the outcome of any other trial.
• Each trial has one of two possible mutually exclusive outcomes: success or failure.
• Each trial has the same probability $(\pi)$ of a ‘success’.
• The probability of a failure is denoted by $(1-\pi)$.
• The random variable $(x)$ is the number of successes in the $n$ trials of the investigation.
• The probability distribution of $x$ is given by:
$$\mathrm{P}(x)=\frac{n !}{x !(n-x) !} \cdot \pi^x \cdot(1-\pi)^{n-x}$$
Where:
$x=$ the number of successes, $0,1,2$, etc
$n=$ number of trials or sample size
$\pi=$ probability of success on each trial

## 统计代写|统计计算代写Statistical calculation代考|The normal distribution

In general, many things are distributed with the characteristics of what we call normal. That is, the majority of the occurrences are in the middle of the distribution, but relatively few on each end. For example, there are relatively few tall people and relatively few short people, but lots of people of average height in the middle. That means the chance (or probability) that a person will be average in height, or more or less in the middle of the distribution, will be much better than the chance that any one person will be either very tall or very short.

Those events that tend to occur in the middle of the normal curve have a higher probability of occurring than the ones in the extreme or tails.

The normal distribution plays a very important role in statistical inference.

• The graph for a continuous random $x$ variable is a smooth curve.
• The curve is unimodal (single mode).
• The distribution is symmetrical around its mean and bell-shaped in appearance.
• The left- and right-hand tails of the distribution extend indefinitely.
• The $x$ axis represents all the possible values of the $x$ variable, which is infinite.
• Two parameters describe the normal distribution: the mean $(\mu)$ describes where the distribution is centred and the standard deviation $(\sigma)$ describes how much the curve spreads out around the centre.
• Probabilities for continuous variables correspond to areas under the normal curve.
• The total area under the normal curve is equal to 1 or $100 \%$ (the sum of all the probabilities of a probability distribution $=1$ ). This means that the areas to the left and the right of the mean will each comprise $50 \%$ of the total area.

# 统计计算代写

## 统计代写|统计计算代写Statistical calculation代考|The binomial distribution

• 实验必须包括 $n$ 相同的试验。
• 这些试验是独立的。也就是说，一次试验的结果不会影响任何其他试验的结果。
• 每个试验都有两个可能的相互排斥的结果之一: 成功或失败。
• 每次试验的概率相同 $(\pi)$ 的”成功”。
• 失败的概率表示为 $(1-\pi)$.
• 随机变量 $(x)$ 是成功的次数 $n$ 调查的审判。
• 的概率分布 $x$ 是 (谁) 给的:
$$\mathrm{P}(x)=\frac{n !}{x !(n-x) !} \cdot \pi^x \cdot(1-\pi)^{n-x}$$
在哪里:
$x=$ 成功次数， $0,1,2$ ， ETC
$n=$ 试验次数或样本量
$\pi=$ 每次试验的成功概率

## 统计代写|统计计算代写Statistical calculation代考|The normal distribution

• 连续随机图X变量是一条平滑的曲线。
• 曲线是单峰的（单一模式）。
• 该分布围绕其均值对称，外观呈钟形。
• 分布的左右尾部无限延伸。
• 这X轴表示所有可能的值X变量，是无限的。
• 两个参数描述正态分布：均值(米)描述分布的中心位置和标准差(p)描述曲线围绕中心展开的程度。
• 连续变量的概率对应于正态曲线下的面积。
• 正态曲线下的总面积等于 1 或100%（概率分布的所有概率之和=1). 这意味着平均值左侧和右侧的区域将分别包含50%的总面积。

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: