9k views

### Does mean=mode imply a symmetric distribution?

I know this question has been asked with the case mean=median, but I did not find anything related to mean=mode. If the mode equals the mean, can I always conclude this is a symmetric distribution? ...
29k views

### Existence of the moment generating function and variance

Can a distribution with finite mean and infinite variance have a moment generating function? What about a distribution with finite mean and finite variance but infinite higher moments?
62k views

### Does mean = median imply that a unimodal distribution is symmetric?

For a unimodal distribution, if mean = median then is it sufficient to say that distribution is symmetric? Wikipedia says in relationship between mean and median: "If the distribution is symmetric ...
18k views