Original subtitles

Instructor: Hi there.

In in this lecture we are going to discuss

the uniform distribution.

For starters, we use the letter U

to define the uniform distribution,

followed by the range of of the values in the data set.

Therefore, we read the following statement as

variable X, follows a discreet uniform distribution

ranging from three to seven.

Events which follow the uniform distribution

are ones where all outcomes have equal probability.

One such event is rolling a single standard, six sided di.

When we roll a standard six sided di,

we have equal change of getting any value from one to six.

The graph of the probability distribution

would have six, equally tall bars, all reaching up to 1/6.

Many events in gambling provide such odds,

where each individual outcome is equally likely.

Not only that, but many everyday situations

follow the uniform distribution.

If your friend offers you three, identical chocolate bars,

the probability assigned to you choosing one of them

also follow the uniform distribution.

One big drawback of uniform distributions

is that the expected value provides us

no relevant information

because all outcomes have the same probability.

The expected value, which is 3.5,

brings no predictive power.

We can still apply the formulas from earlier

and get a mean of 3.5 at a variance of 105 over 36.

These values however, are completely uninterpretable

and there is no real intuition behind what they mean.

The main takeaway is that when an event is following

the uniform distribution, each outcome is equally likely.

Therefore, both the mean and the variance

are uninterpretable and possess

no predictive power whatsoever.

Okay, sadly, the uniform is not the only

discreet distribution, for which we cannot construct

useful prediction intervals.

In the next video, we will introduce

the Bernoulli distribution.

Thanks for watching.