IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
A simple random walk starts at 0. At each step it moves up 1 with probability 0.6 and down 1 with probability 0.4, independently. What is the expected position after 50 steps?
The expected position is 10. Each step has expected value 0.6 minus 0.4, which is 0.2, and expectations add over independent steps, so 50 steps give 50 times 0.2, equal to 10.
- A5
- B10Correct
- C20
- D30
- 50
Explanation
Each step has mean 0.6(1)+0.4(-1)=0.2. Over 50 steps the expected position is 50 x 0.2 = 10. The value 20 comes from using only the up-probability gap of 0.4 per step, which is wrong.
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