The electron will behave more like a wave than a particle, with its position described by probability distributions that you'll have to imagine.

电子的行为不像粒子，而更像是波，想像它出现的位置以机率分布。

This is the variance of your original probability distribution.

这是原始概率分布的方差。

And let me draw its probability distribution.

让我画出它的概率分布。

All you can know is a probability distribution of where it is likely to be.

您所知道的只是它可能所在位置的概率分布。

He views people not as good or bad, but as " probability distributions" around a mean.

他认为人不是好是坏，而是围绕平均值的“概率分布”。

I discuss why a likelihood is different to a probability distribution in basic inference.

我将讨论在基本推理中为什么可能性与概率分布不同。

And I focus on the methods which are required to independently sample from a probability distribution.

我主要讲从概率分布中独立抽样所需要的方法。

Really the typical way in which it stated is in terms of probability distribution.

它最典型的表述方式是概率分布。

So what can we do? Well, it turns out that one way of understanding a probability distribution.

那么我们能做什么呢 这是理解概率分布的一种方法。

The probability of getting any x, and it's a class of probability distribution functions.

得到任意x的概率，是一类概率分布函数。

And this also applies to the discrete probability distributions.

这也适用于离散概率分布。

What I have just drawn is a binomial probability distribution.

我刚才画的是二项式概率分布。

This is a discreet probability distribution of me making, in this case, k shots out of 6.

这是我做出的谨慎概率分布，在这种情况下，6 次中有 k 次。

So this is the sum over the entire probability distribution, and so that is going to be equal to 1.

所以这是整个概率分布的总和，所以它等于 1。

And this, together with some of the other difficulties of dealing with high dimensional probabilities distributions, mean that.

这个 加上其他一些处理高维概率分布的困难 意味着。

It's a particular instance of the binomial probability distribution.

这是二项式概率分布的一个特例。

So that's my probability distribution function.

这就是我的概率分布函数。

Well, you can look at the probability distribution, the discreet probability distribution.

嗯，你可以看看概率分布，离散概率分布。

But that's my discrete probability distribution function.

但那是我的离散概率分布函数。

It isn't true for any random variable, X. Only true for random variable, X, whose probability distribution is the binomial distribution.

它不适用于任何随机变量 X。仅适用于概率分布为二项分布的随机变量 X。