FIN312: Mathematics and Programming for FinTech Assignment, SUSS, Singapore In Dice Game, you must run across a 140m bridge before it collapses. You are given two 6- sided dices with these numbers on their faces
In Dice Game, you must run across a 140m bridge before it collapses. You are given two 6- sided dices with these numbers on their faces:
-8, -7, 1, 2, 7, 8 on the first dice
-7, -2, 1, 3, 7, 7 on the second dice
At every move, you throw the two dice simultaneously to obtain a score of X which is the product of the top faces of the two dice. You are then required to run forward X meters across the bridge. If unfortunately, X is negative, you need to run backward X meters.
You can only make 3 moves before the bridge collapses.
For example, if you throw (8, 7), (2, -2) and (-7, -7), you will have run a total of 101m (since 8 x 7 + 2 x (-2) + (-7) x (-7) = 56 – 4 + 49 = 101). Sadly, this means you will still be on the bridge when it collapses.
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You are not allowed to import any packages in this question unless stated otherwise.
(a) List the unique scores X you can get per move in ascending order.
(b) Code a function pmf(x) that returns P(X = x). Compute to 6 decimal places the values
P(X = -21)
P(X = -14)
P(X = 14)
P(X = 50)
(c) Code a function cdf(x) that returns P(X x). Compute to 6 significant figuresthe values
P(X -21)
P(X < -14)
P(X
P(X < 50)
(d) What is the probability of you crossing the bridge successfully? Explain your reasoning clearly. Give your answer correct to 6 significant figures.
(e) Draw and label the step graphs of pmf(x) and cdf(x) for an integer x such that – x matplotlib.pyplot.
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