Yep, they can be one or the other - male or female that is - or both. The self-pollinating varieties are becoming more common now and almost always if you buy one from a nursery it will be.
But it's hard to tell from the flower if it is a "perfect" flower. That one is either a female flower or a "perfect" flower meaning it may have both stamens and pistils. The only way to tell for sure other than to dissect one of the flowers and look at it under a microscope (your County Extension has one, no doubt) is to see if it makes a fruit all by itself. You can try helping it by taking a tiny artist's paintbrush and diddling the pollen around a bit.
Did you grow this from a seed, or buy it already started? If grown from a seed, even if the parent was a self-pollinating type, the offspring won't necessarily carry the trait.
