What are the differences between z-distribution and t-distribution?
In probability and statistics, Student's t-distribution (or simply the t-distribution) is a probability distribution that arises in the problem of estimating the mean of a normally distributed population when the sample size is small. It is the basis of the popular Student's t-tests for the statistical significance of the difference between two sample means, and for confidence intervals for the difference between two population means. The Student's t-distribution is a special case of the generalised hyperbolic distribution. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Normal distributions can be transformed to standard normal distributions by the formula:
In short, the Z-distribution is a way of naming the Standard Normal distribution.Assuming your next question is “..ok then, so what is the difference between the Normal and Normal Standard”;(I’m going to go ahead and copy a bit of a prior answer instead of pasting the link to it).The Standard Normal Distribution is a specific instance of the Normal Distribution that has a mean of ‘0’ and a standard deviation of ‘1’.The visual way to understand it would be the following image (taken from here):The four curves are Normal distributions, but only the red one is Standard Normal (since it’s mean is zero, which means that’s where it’s centred, and its standard deviation is one, which basically tells us “how much the bell opens” to put it colloquially).So, if one is just a specific instance of the other, what purpose does the distinction serve?Suppose you have a data set of scores which are normally distributed with a mean of 86 and a standard deviation of 14. You pick a random test without looking at the score and you want to know the probability the score was below… say 72.What you can do is take the probability density function;and calculate the probability P(X<72) integrating on this function from -∞ to 72, replacing your SD and mean on the function. But it is a tedious integration at best.Instead, if you standardise your function then you can get it much easier.To do this, you subtract the mean from the value you want to examine (in this case 72) and you divide by the SD. So:[math]P(X<72) = P(X < (72−86)/14 )= P(X<−1)[/math]So now you know that P(X<72) on your own Normal Distribution is equivalent to P(X<-1) on the Standard Normal Distribution.You are now interested in the area of the region which is left to the -1 (which as you can see is .1587 or 15.87% probability that the score is lower than 72).To get this value you can integrate on the SND density function or (much preferably) you can search on the normal distribution table or Z-TABLE (re-connecting with your original question) which resumes the results of many possible evaluations so you don’t have to integrate.In this case, you just look for the -1 on the left and the 00 on the top (because it is -1.00) and you can see that the probability is .1587.Hope it helped.
Michael Lamar gave a great answer and it’s hard for me to add to it. But one additional difference is that, while the normal distribution shows up frequently (at least approximately) in nature, the continuous uniform distribution doesn’t.The discrete uniform distribution shows up sometimes, but it’s hard to think of an example of a natural variable that occurs in nature.Another difference is that coming up with the normal distribution took some serious brain power. I mean, just look at the PDF! :[math]\frac{1}{\sqrt{2 \pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}[/math]or look at its history of development - its chief developers were LaPlace and Gauss, two of the great mathematicians of history.Another thing is that the normal distribution has 0 skew and 0 excess kurtosis. The uniform does not.
What's the difference between Poisson Distribution, Binomial Distribution and Normal Distrib. ? Use examples!
In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, AND the Poisson distribution is also a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume. I hope this will be enough.
Zoe, you will know that Student’s T-test for statistical significance is the original such test. The Z-test makes assumptions which simplify the calculation and it is attractive for that reason. (My personal opinion is that there is nothing onerous about a T-test and it will always work.)The Z-test assumes normal distribution but the T-test can cope with non-normal distribution. It is generally accepted that a Z-test is valid for any sample where n>30. When a sample is 30 or less it is essential to use the more sophisticated T-test to get a reliable result. If the sample size gets too small a reliable result is not attainable.The whole subject of tests for statistical significance is a very large one and goes well beyond the reasonable limits of a QUORA answer. I strongly recommend that you look at the relevant videos from the Khan Academy. They are first rate.
When the degrees of freedom are large, there is not much difference between the t- and the z-distributions. The term “bell curve” would apply equally badly to both distributions (look at a section of a real bell). The t-distribution with one degree of freedom is also known as the Cauchy distribution. It has no moments so the mean is undefined. In general there are moments up to order [math]\nu-1[/math] where [math]\nu[/math] is the number of degrees of freedom.The density function of the standard normal distribution is [math]\frac1{\sqrt{2\pi}} e^{\frac1{2}x^2}[/math] which the density of the t-distribution is [math]A{\left(1+\frac{x^2}{\nu}\right)}^{-\frac{\nu+1}{2}}[/math] where [math]A = \frac{\Gamma\left({\frac{\nu+1}{2}}\right)}{\sqrt{\nu\pi}\Gamma\left(\frac{\nu}{2}\right)}[/math].
A population distribution is a distribution in which every single member of some group is measured on some attribute and then that attribute is plotted. If you took every single human on earth and measured the height of each person and then plotted the results with Number of People on the vertical axis and Height on the horizontal axis, you would have the distribution of height in the population.A sampling distribution is a distribution of values representing the samples they were obtained from. Sampling distributions are always based on samples of the same size (e.g., all samples have 10 or 100 or whatever number in them, N[math]1[/math] = N[math]2[/math] = … =N[math]N[/math]). Suppose, you selected 1,000 people randomly from every country in the world and measured their heights. The sampling distribution would have one value representing each country and could be a distribution of mean sample heights, or variance or range of the heights in a sample, or median sample height, or anything else you can calculate from the heights in a sample. In all of these instances, Number of Samples is what gets plotted on the vertical axis.I remember bashing my head on this one in my first statistics class. Hang in, you’ll get it. :-)
Discuss the similarities and differences between normal, t and F distributions.?
The normal distribution has 2 parameters, the mean, µ, and the standard deviation, σ. It is bell-shaped and usually results from errors in measuring something. When used as a probability distribution it is difficult to integrate and the probabilities exist in a standard normal table with µ = 0 and σ = 1. It is widely used in many scientific areas. The t-distribution resembles the normal distribution except it is flatter and wider. It has characterized by sample mean, Xbar, sample standard deviation, s, and the degrees of freedom, n-1. This has the same applications as the normal distribution, but is used when small samples (n < 30) are taken to estimate the mean of a near-normal population. The F-distribution is the ratio of 2 variances, take from normal distributions, and is used to compare 2 variances and, in that capacity, is widely used in analysis of variance (ANOVA) experiments. It has 2 parameters, the degrees of freedom of the 2 distributions.
They are the switches for heavy duty.In fact, a core switch can do the same things a normal switch does: forwarding traffic to devices. The core, however, can do that gororr devices, a huge load of them. A core switch can handle an entire Enterprise or data-center.This means they have a lots of ports, a lot of power and a lot of redundancy. They have redundant PSU, and each component is designed to be redundant. They don't come with a fixed number of ports, but with slots where you can insert ports of the type you like.There is also a great difference in the process, of course…To learn the details, check out this guide: The network device: form factor and console access.