A fair four-sided die has its sides labelled U, D, L, and R, respectively. A tok

Question

A fair four-sided die has its sides labelled U, D, L, and R, respectively. A token is placed at (0, 0) on the Cartesian plane and the die is then rolled repeatedly. After each roll, the token is moved as follows: Let the random variable Y_n be the taxicab distant* the token is from (0, 0) after n greaterthanorequalto 0 rolls and the consequent moves. It should be pretty obvious that Y_0 = 0: the token starts at (0, 0) and n = 0 moves have taken place. After that it gets more interesting What is E(Y_n)? Explain why test you can. What is V(Y_n)? Explain why as best you can. A fair four-sided die has its sides labelled U, D, L, and R, respectively. A token is placed at (0, 0) on the Cartesian plane and the die is then rolled repeatedly. After each roll, the token is moved as follows: Let the random variable Y_n be the taxicab distance* the token is from (0, 0) after n greaterthanorequalto 0 rolls and the consequent moves. It should be pretty obvious that Y_0 = 0: the token starts at (0, 0) and n = 0 moves have taken place. After that it gets more interesting

Explanation / Answer

Y = b + a

Y value changes as die changes its value .

Let Y(i) - Value of Y (it may be corresponding to U / D / L / R ) at ' i ' th time die is rolled.

n – No : of times die is rolled

E(Y) - Mean of the values obtained by Y or the value which is most repesentative of all values .

                  = Sum of all values of Y / (no: of times die is rolled )

                 = Yi / n .

V (Y) – Variance of Y – a measure of deviation from centered value

= ( ( instantaneous value of Y ) ² - ( of all value of Y )²/n ) / (n-1)

= ( (Y(i))² - ( Y(i))²/n ) /   (n-1) .

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