Question

A robot is given 1 random instruction every second for 10 seconds. Each

instruction will be either a command to move 1 inch to the left, or 1 inch

to the right. The likelihoods of the instruction being a command to move

to the left and right are 'p' and '1-p', respectively.

a) What is the expectation of the robot's final position with respect

to its starting position.

b) What is the variance we might expect for observations of the

robot's final position?

c) For what value(s) of 'p' is this variance greatest?

d) For what value(s) of 'p' is the expectation of net distance traveled greatest?

e) For what value(s) of 'p' is the total number of inches moved greatest?

Answer 1