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Problem 1 Medium Difficulty

In what ways is the $t$ distribution similar to the standard normal distribution? In what ways is the $t$ distribution different from the standard normal distribution?

Answer

The t distribution is similar to the standard normal distribution in the following ways. 1. It is bell-shaped. 2. It is symmetric about the mean. 3. The mean, median, and mode are equal to 0 and are located at the center of the distribution. 4. The curve approaches but never touches the x axis.

The t distribution differs from the standard normal distribution in the following ways. 1. The variance is greater than 1. 2. The t distribution is a family of curves based on the degrees of freedom, which is a number related to sample size. (Recall that the symbol for degrees of freedom is d.f.

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Video Transcript

Hi, Uh, for the similarities, there are four main similarities between C distribution and distribution. The 1st 1 Both of them, have, um, a bill shape, um, distribution So that the distribution and his team the 2nd 1 the 2nd 1 is they are symmetric on the mean Hey, what you'd really we call it a mule? The 3rd 1 is that's the mean media and board are equal to zero. So cynical zero would also more media on. Don't forget that. The mean also is centered for both cases. The 4th 1 is that's the care approaches but never touch the X axis. So if we have a new extension off off the the bill care is gonna approach to the X axis at never touch the X axis for the differences. The first differences that the variants, um, is greater than one anti distribution. The 2nd 1 is that t distribution is family off cover curves that based on degree of freedom. So we have something called to get your freedom and scores equal toe in minus one. Ah, but indeed the solution We don't have this. The 3rd 1 is that as the sample size go to infinity, T is gonna approach toe normal solution. Thank you.