Probability

Lets define exponential smoothing first...

Exponential smoothing, or exponential moving average, is a running average of a set of observations, where the weight of each observation is inversely exponentially weighted as a function of how old it is. It is a relatively simple thing to do.

Given a set of observations O1, O2, O3, ... ON the running exponential moving average A1, A2, A3, ... AN can be calculated in real time, at each time N, with the expression ...

AN = AN-1 (1 - X) + ON X

... where X is a weighting factor that determines that amount of smoothing. For instance, if X were zero, then the smoothing is infinite, and O does not contribute at all to A, and if X were one, then smoothing is zero, and A follows O with no smoothing at all. In a more useful example, if X were 0.2, then the smoothing would be five, and A would follow O with a time constant of five iterations, i.e. after five iterations we would be at about 63% of one step change and after 25 iterations we would be at about 95% of one step change.

Some people swap the position of X and (1 - X) in the above equation. Its their choice, but the discussion that follows will have to change accordingly.

X is the smoothing factor. It is simply the number of iterations that you want for your time constant. If you were to model this as an electronic circuit, for instance, with a capacitor and a resistor, the exponential curve would be in the form ...

e-T/RC

... where RC was your time constant. The same thing applies here. If you evaluated the first equation once per second, with an X value of 0.2, you would have a time constant of 5 seconds. If you, on the other hand, evaluated it 100 times per second, with X being 0.002, you would still have a time constant of 5 seconds, but it would much more closely approximate the second equation, which is a continuous equation, rather than a discrete equation.

In summary, then, the smoothing factor, or X, is one over the number of iterations that you want to be your time constant.

the area between .79 and 2.67 = .4962-.2852

= .2110

It means just what it seems to -- someone tosses a coin up and you try to guess which side will be facing up when it lands. "Heads" is the side with the person's face on it and "tails" is other side.

No. The simple answer is no. No matter what you do, even if there are no enemies around when it happens, Chopper will still get hit by a missile and crash into the stadium after the ejection system fails. If you check the replay at the time Chopper says that he was hit and switch the view to Chopper's plane, you'll see that it never gets hit. It is just a requirement for the plot. I hate it, too.

For a discrete distribution, if n trials are carried out and if x of them are favourable to the event that you are interested in, then the probability is x/n. Note that it may be possible to work out n and x on theoretical grounds rather than actually doing the experiment.

The formula gets more complicated for continuous variables. For continuous variables, it is the area under the probability density curve over the domain of interest.

Provided the samples are independent, the Central Limit Theorem will ensure that the sample means will be distributed approximately normally with mean equal to the population mean.

33

There is no formula: it is a process of swapping letters in a systematic manner.

The probability of getting two tails is 1/4.

The probability of something happening is the answer to the question, "What fraction of the time will this happen?" It is the number of ways it can happen, out of all the different things that can happen.

With two coin flips, these are all the things that can happen

H H

H T

T H

T T

There is one way in which you can get two tails, out of four possible things that can happen. One out of four, or 1/4.

You have six different letters. They can be arranged in 6 x 5 x 4 x 3 x 2 = 720 different ways.

The sample is of little use in making estimates for the population as a whole unless it is known exactly how it is non-representative.

1/16

The likelihood that a particular event will occur is called probability. It quantifies the chance of that event happening, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability can be represented as a fraction, decimal, or percentage, and is used in various fields, including statistics, finance, and science, to assess risks and make predictions.

Zero

Ok probabilty is easy once you get to know how to do it. Ok so have you ever picked a colored marble ou of a bag? well that's probabilty you will have a guess of what color you will pull out. That is how you do probabilty

Awful question.

There are 720 possible permutations.

A negative z-score indicates that the observed value (or statistic) was below the mean. In non-directional tests, a negative z-score is just as likely as a positive one.

1

A square is a plane (flat) shape whose boundaries are four straight lines of equal length such that these lines meet, in pairs, at four points (vertices). At these vertices they form angles of 90 degrees. The diagonals of the square are straight lines joining opposite vertices. These diagonals meet one another.

The given statement means that the angles formed at the crossing points of the diagonals measure 90 degrees.

Yes, probably is a proposition. Because it is expounding upon something previously said.

5/9

Yes, it is possible.

No, you could not be sure. There would be a high probability that you would roll ten but with a random event, you can never be sure of a specific outcome such as that.