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Binomial:

1. A single trial has only 2 possible outcomes: success or failure

2. A fixed number of trials, n

3. Trials are independent

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In order to integrate (cosx)^3, there is no given rule (by-parts, 'try' method, chain rule) which we can follow. We would need to split it into (cosx)^2 and cosx. Then use the identity: (sinx)^2 + (cosx)^...

We can think of any solution of this equation as a string of twelve 1's and two 0's. For example, one such solution could be a=6, b=2 and c=4. In this case we would write the solution as 11111101101111. W...

This is a typical C4 differential equation question. The same algorithm could be used for a lot of other problems.

First of all, from the hint we have that dH/dt = -kH (1).

We need to separa...