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What are the conditions required for the poisson distribution?

Events must be random and independent of each other. There must be a uniform rate of occurance.

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'Find the first derivative, with respect to x, of arctan(1/x) for non-zero real x. Hence show that the value of arctan(x)+arctan(1/x) is constant for all non-zero x, explicitly stating this constant in your final answer.' How do I solve this?

f(x) = 9x^3 – 33x^2 –55x – 25. Given that x = 5 is a solution of the equation f(x) = 0, use an algebraic method to solve f(x) = 0 completely.

Understanding differentiation from first principle.

prove by induction that, f(n) = 2^(3n+1) + 3(5^(2n+1)) is divisible by 17 for all n>0.

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