A Random Walker

Bro is handsome

This is a easy problem on a line isn’t it. Because if X is the position after n time steps, the probability that X=k is kind of just a Binomial RV.

Easy peasy

clear

It is important to reiterate the information given in this short lecture about the conditions that exists in the problem
1st condition: Independent Events,moving in a certain direction does not affect the next choice movement event i.e. unbiased decision [P(BF)= P(B)xP(F)]

2nd condition: Mutually exclusive event,If moved to the direction of F it exclude the possibility of moving to the direction of B i.e one decision eliminates the other

[P(FB,BF) = P(FB)+P(BF)]

The last part was specific for the problem,while the above are general

3rd condition: Conditional probability,the movement was forward given that the end point is position 1.

This is one of those problem where there is a combination of 3 fundamental concepts of probability at the same time.

Great work MIT

I found it super relaxing to watch! Thank you

the sound is not good I am quite disappointed

Are the last step of each possibilities independent from the previous one ,such as if I take F then taking the B step is inevitable .then the p(B) must be 1 provided we have to end up at that same position we started ....I have some confusion in this step.

I don't even know how i ended up here, but I understood most of this stuff.

Is DZ video wt iam looking for 😏

what was the problem?

Thank you so muchh

Kuang Xu is a genius.

what about if you have another, 1-p-q, a circulation