down up up up up up until the end what's the probability of that well we can write it out if we say it probably of up is theta then the probability of up down down all up would be theta times one minus theta times one minus theta times theta and this would be seven times one time in this two times and so total we'd have data to the eight times one minus theta squared as the probability of that particular sequence happening we'll call it as the likelihood of what we saw happen if we choose a parameter vector theta then we could say well how should