A user interface allows a user to freehand draw a probability density curve, or to select from predetermined probability densities, such as a normal distribution. The probability density represents the user's opinion regarding the probability of occurrence for different outcomes of a future event. The user can easily manipulate the shape of the probability density by dragging portions of the curve using an input device, such as to change the mean or standard deviation. Further, a scoring rule is applied to the probability density so that an updated score is displayed as the probability density is manipulated. The probability density can be input to an estimate contest or a prediction market, for instance. The user interface can also allow the user to freehand draw a scoring curve from which a probability density can be computed based on a scoring rule.