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Statistics: What is the difference between a Binomial and Poisson distribution?

Binomial: A single trial has only 2 possible outcomes: success or failure A fixed number of trials, n Trials are independent The probability of success remains constant at each trial Mean: E(x) = np Var(x) =...
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Answered by Shivani S. • Maths tutor
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Integrate (cosx)^3

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)^2 =...
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Answered by Shivani S. • Maths tutor
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How many solutions are there of the equation a+b+c=12, where a,b,c are non-negative integers?

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. Writ...
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Answered by Brendan M. • Maths tutor
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A tank is filled with water up to the height H0. At the bottom of the tank, there is a tap which is opened at t=0. How does the height of liquid change with time?(Hint: dH/dt is proportional to -H)

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 separate the variables ...
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Answered by Maxim B. • Maths tutor
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Find the coordinate of the turning point of the curve y = x^2 - 10x + 7, by completing the square

First, we need to complete the square. We take the first part of the equation ignoring the constant ( + 7). y = x 2 - 10x , we want to change the form of this equation from x 2 + ax + (a/2) 2 into ( x + a/2 ...
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Answered by James P. • Maths tutor
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