In a random walk an object takes sequential steps in a random directions. While

Question

In a random walk an object takes sequential steps in a random directions. While one might expect the result to land back at the origin, on average the object slowly moves away from the origin. Below is a 10 step random walk for an object that begins at the origin of a Cartesian coordinate system and takes 1 unit steps in random directions. How far does the object end up from the origin?

x-step y-step table

-0.88 0.47

-0.29 -0.96

-0.98 0.18

-0.84 0.54

0.99 -0.07

-0.99 0.09

0.74 0.67

.63 -0.78

-.55 0.84

-0.41 0.91

Explanation / Answer

Final x co-ordinate = X = sum of x-steps

X = -0.88 -0.29 -0.98 - 0.84 +0.99 -0.99 +0.74 +0.63 -0.55 -0.41

X = - 2.58

Final y co-ordinate = Y = sum of y-steps

Y = 0.47 - 0.96 +0.18 +0.54 -0.07 +0.09 + 0.67 -0.78 + 0.84 +0.91

Y = 1.89

Total distance = ( X2 + Y2)0.5

= ( 2.582 + 1.892)

= 3.198

So the man is 3.198 m far away from initial position

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.