I think it is incorrect to say that Y cannot be 0 (since it is a normal random variable with mean 0). However, we can say that the random variable X/Y is almost surely continuous and well-defined everywhere. This is because although Y can take the value 0, the probability with which it does so is also 0 (since it is the probability that a continuous random variable takes a discrete value).
it could be. remember that normal distribution is standarization version of distribution so, naturally all of that variable wasnt zero from beginning with.
Thank you for the video. I have a question that I was hoping that you could answer. if x and y have normal distributions with non-zero mean and standard deviation which is not equal and not 1, how can I calculate the PDF of Z=X/Y?
Great video!!! With clear and logical explanation. Im planning to look every videos in your probability playlist. I have some questions. Since X and Y are standard normal, when you construct r.v. T, why did you say that y cant be zero? And also why cant T be zero (when x is zero)?
my brain hurt
I think it is incorrect to say that Y cannot be 0 (since it is a normal random variable with mean 0).
However, we can say that the random variable X/Y is almost surely continuous and well-defined everywhere. This is because although Y can take the value 0, the probability with which it does so is also 0 (since it is the probability that a continuous random variable takes a discrete value).
it could be. remember that normal distribution is standarization version of distribution so, naturally all of that variable wasnt zero from beginning with.
I didn't get the division . Why the division what's the intuition there
I did not get what you meant divide by area
Very good 😀
Thank you for the video. I have a question that I was hoping that you could answer.
if x and y have normal distributions with non-zero mean and standard deviation which is not equal and not 1, how can I calculate the PDF of Z=X/Y?
very good video. really
Why y(s) is not equal to zero
Great video!!! With clear and logical explanation. Im planning to look every videos in your probability playlist.
I have some questions. Since X and Y are standard normal, when you construct r.v. T, why did you say that y cant be zero? And also why cant T be zero (when x is zero)?
+Teerapat Jirasirikul If Y would be zero then x/y will be infinite