Example 3.2.2 Temperature Forecasts. Television weather forecasters announce high and low temperature forecasts as integer numbers of degrees. These forecasts, however, are the results of very sophisticated weather models that provide more precise forecasts that the television personalities round to the nearest integer for simplicity. If we wanted to know what temperature X the weather models actually produced, it might be safe to assume that X was distributed uniformly on the interval from y-1/2 to y+1/2, where y was the integer forecast announced on television.