A particle starting at the origin once every second has a 1/6 probability of jumping two steps forward, a 1/6 probability of jumping one steps forward, a 1/3 probability of jumping one step back, and a 1/3 probability of staying in the same place.
Calculate the probability that at the 36 second mark the particle is more than ten units away from the origen.
I've messed around with this problem and think the expected value is +6 units from the origen and the variance is 41 but I don't know what to do to actually figure out the probabilities here. Thanks.
Unless someone has a better non-super intensive method; we use the Central limit theorem which states the successions of i.v. when the reach a large enough number tend to resemble a normal distribution. Thus the z-point value are .625 and -2.5 respectively and that results in a .006 prob of being in the left tail and a .266 prob. of being in the right tail which gives us .272 prob. of being 10 or more units away from the origin.