Create a function that takes three arguments prob, prize, pay and returns true if prob * prize > pay; otherwise return false. To illustrate: profitableGamble (0.2, 50, 9) ... should yield true, since the net profit is 1 (0.2 * 50 -9), and 1 > 0. Examples profitableGamble (0.2, 50, 9) → true profitableGamble (0.9, 1, 2) → false profitableGamble (0.9, 3, 2) → true

Asymptotic function relationships. Verify each of the following statements by the definitions to see if they are true or false 1. If ?(?) = Θ(?), then ??(?) = Θ(?2 ) 2. If ?(?) = ?(?2 ) and ?(?) = Ω(?(?)), then ?(?) = ?(?2) 3. If ?(?) = ?(0. 5?2 ) and ?(?) = Ω(7?2 + ?????), then ?(?) = Θ(?2 ) 4. If ?(?) = ?(?3 ), then ?(?) = Ω(2?3 ) 5. If ?(?) = Θ(?3 ), then ?(?) = ?(2n )

Return a lambda function that takes in multiplier (the multiplier is a number) and returns a lambda function that will take in another number and will return the new input multiplied by the multiplier. def higher_order_lambdas(): Return a lambda function that takes in a multiplier and returns a lambda function that given an input return the input multiplied by the multiplier >>> hol = higher_order_lambdas () doubles = hol(2) >> doubles (3) 6 >>> hol = higher_order_lambdas() >> triples hol(3) >>> triples (4) 12 = "*** YOUR CODE HERE ***"

Implement a function or class to solve the Black-Scholed Model Partial Differential Equation. It should be able to price both European and American-style derivatives of arbitrary payoff structure (i.e. the payoff function should be a Callable). Implement full functionality: That is, calculate the price of both European and American options on dividend-paying stocks and be flexible to price other options besides standard calls and puts. Provide documentation: Provide docstrings and example usage for your implementation. It should be easy for someone looking at your code to understand how to call it and what the parameters mean. A short README.md file or example script would be useful.