You need to rebuild their trust in you. This can take time, and it also depends on the magnitude of the mistrust you brought upon yourself. You have to show them how mature you are by becoming responsible and taking charge in the appropriate circumstance.

Instead of worrying about them worrying about you and the 'stupid things' you have done - worry about becoming the kind of person who does NOT do 'stupid things' and the rest will follow....

Like most things, communication is a large key here. Only 2 stupid things is a matter of perspective. For parents one stupid thing in 18 years is usually enough to make them think it was an unforgivable malign against their ability to raise their own offspring. Your parents will likely not lay off until three things happen. One, you prove that in a clinch situation, you do the right thing and not the wrong thing when the wrong thing was far easier to do. This is usually an event of opportunity. You can't seek it out, it will just happen and your moral decision should be automatic. For example, another young person in your room wants to engage in physical intimacy while your parents are away. If you are able to overcome personal desire (assuming personal desire outweighing the desire to please one's parents) then by relaying this struggle against temptation to one's parents, they can rest assured that you can repeat this and no one is getting pregnant or HIV short of forced carnal knowledge. Two, you prove that you can handle yourself and that your parents care for you is no longer a necessity but a grace. That is, you appreciate their help but in the event that they were to disappear, you can survive and persist and continue to make them proud. This is a proactive event. This usually involves getting a job that is both satisfying and has potential. Burger flipping, while an opportunity, is not the kind of opportunity that will make your parents think that they won't have to pay for their grandkids. Third, you prove that they are unreasonably paranoid about your behavioral/moral/social propensities. This means that they have to see that their views on you are skewed from not knowing you well enough as a person. This is also a personally initiated event, likely more effective after the previous two conditions have been fulfilled. This includes sitting down and talking with one's parents, having a teacher, coach, other mentor, or trusted friend (one who they think is awesome) giving a testimonial, or achievement of a community honor for good works done, such as an award for 1000 hours of community service. If you do not fulfill any of the three above requisites, please seriously reconsider what warrants "being too hard on you." Once upon a time, children were belt whipped for talking out of turn at the table, while today drinking alcohol underage and driving without a license being punished with a month's restriction and a year of therapy is considered "excessive". If any minor can provide all three of the requisites outlined above, then they are mature (practically age of majority) person in my book. However, they can be like my parents and dog me into adulthood in spite of all the evidence to the contrary.

Trust, once lost, can be very difficult to regain. As others have said, you need to show by your actions that you are worthy of trust. You have done a couple of stupid things. Depending on the seriousness of the these things it could take quite a bit of time re-earn their trust. The thing to do is to show that you learn from you mistakes and not do them again. Given enough time you will earn their trust again and they will let up.