I am analyzing a timing circuit I designed, and I need to calculate the probability of a certain event (bit error). For example, I have derived this equation:
$(1 + x) / d < 1 / M$,
where x is a random variable with a normal distribution, d is a random variable with uniform distribution, and M is a constant.
I would like to be able to calculate the probability that this inequality is true, for a given distribution for x, a given distribution for d, and a given M. For example, let's say x has a normal distribution with mean = 0 and SD = 0.05, d has a uniform distribution between 0 and 1, and M = 3. How would I calculate the probability that the inequality is true?
If there was a single random variable, I could do it. But I am lost and don't know how to solve it. I tried searching and reading a statistics textbook, but I don't know what to look for.