Please answer parts (e),(f),and (g) only.

This is question regards on the statistics and mathematics concept. Please show me the step-by-step solution. 2. Consider the following game of chance. Initially, a player is given a single token. During each turn the player rolls a 6-sided dice. If the result is a 1 or 2 the player discards a token. If the result is a 3 or 4 the player picks up an additional token. If the result is a 5 or 6 the player picks up an additional two tokens. The game ends in a win if the player discards all tokens and a loss if the player accumulates four or more tokens. At any given time the player is in one of five states W, T, 27, 37, L. .W : Player has 0 tokens and has won the game (absorbing state). T : Player has 1 token. 27 : Player has 2 tokens. 37 : Player has 3 tokens. L: Player has 4 or more tokens and has lost the game (absorbing state). (a) Draw a state transition diagram. (b) List all state sequences that lead to a win in exactly 6 turns. (c) Calculate the probability of each state sequence listed in part (b) and use the results to calculate the probability that a player wins the game in exactly 6 turns. P(Sk=W)] P(Sk = T) (d) Set Pk P(Sx = 2T) . Find an initial probability vector po and a transition matrix A P(Sk = 37 P(Sk = 1) such that for all k> 0 we have Pk+1 = Apk (e) Use Python to calculate pe and p5. Use the results to verify your answer to part (c). (f) Use Python to calculate P1000- (8) Use the numerical evidence from part (f) to conjecture the value of the following limits. Probability of Winning Game = lim P(Sx =W) = Probability of Losing Game = lim P(Sk = L) =