Probability and Markov Processes? Free Throws. Please Help.

Question

If she made the last free throw, then her probability of making the next one is 0.9. On the other hand, If she missed the last free throw, then her probability of making the next one is 0.2.

Assume that state 1 is Makes the Free Throw and that state 2 is Misses the Free Throw.

(1) Find the transition matrix for this Markov process.

 

The matrix must be a 2x2.

Answer 1

 

Hi Katie,

 

Let S_i, i = 1, 2, denote the state i.

 

If T_ij denotes the transition from S_j to S_i,

transition probabilities are given as follows.

 

     Prob(T₁₁) = 0.9

 

     Prob(T₂₁) = 1- Prob(T₁₁) = 1 - 0.9 = 0.1

 

     Prob(T₁₂) = 0.2

 

     Prob(T₂₂) = 1- Prob(T₁₂) = 1 - 0.2 = 0.8

 

So, the Markovian transition matrix is

 

     ⌈ 0.9     0.2 ⌉

     ⌊ 0.1     0.8 ⌋