Suppose $Y \sim \mathrm{Bin}(n,p)$ given $\Theta=(p,q)$ and $Z \sim \mathrm{Bin}(y,q)$ given $Y=y$ and $\Theta=(p,q)$. Now I want to determine the varianc...

I have to find out the derivative of given function by using 'first principle method', but the question has eaten half of my brain, the problem ...

A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700 rad/seconds squared. How many revolutions does it make before stopping? If only I ...

For all non-zero integers $x,y,z$ clearly there exist infinitely many non-zero integers $a,b,c$ such that $$ax+by+cz=0$$ How can I prove this simple state...

The set of real values of $x$ satisfying the equation $\left[\frac{3}{x}\right]+\left[\frac{4}{x}\right]=5$,(where $[]$ denotes the greatest integer funct...

I have known about Zeno's paradox for some time now, but I have never really understood what exactly the paradox is. People always seem to have diffe...

I am trying to make the link between the population variance, $\sigma^{2}$ and the sample variance $s^{2}$ with a particular example. Say I have a populat...

Let $\{X_t\}_{t\ge 0}$ be a Poisson Process with parameter $\lambda$. Suppose that each event is type 1 with probability $\alpha$ and type 2 with probabil...

How to calculate $$\sin(37°)$$ with a Taylor approximation accurate to 3 decimal digits? I know it is not a difficult question, but I have no answers of m...

Can someone check my work on this problem? I'd like to be able to figure out how fast cars are going by measure the time it takes to pass me, or for ...