Thank you for your reply.
I know that the probability distribution of the sum of two or more random variables is the convolution of their individual pdf's, but as far as I know this is only valid for independent random variables. While ##E(aX+bY)=aE(X)+bE(Y)## is true in general, right?.
1. Homework Statement
Show that the expectation operator E() is a linear operator, or, implying:
E(a\bar{x}+b\bar{y})=aE(\bar{x})+bE(\bar{y})
2. Homework Equations
E(\bar{x})=\int_{-\infty}^{+\infty}xf_{\bar{x}}(x)dx
With f_{\bar{x}} the probability density function of random variable...
1. Homework Statement
1: Determine the wall shear stress that acts at the lower side of the plate.
2: Determine the force Fx that is needed to give the plate a speed of u = 1m/s.
3: Determine the speed V, that is leaves an air jet that blows against the plate and which creates the same force...
Thank you for your reply.
But now I wonder, how is the mean flow of the element defined? If we look at a flowing liquid (for example water), now we can theoretically draw a fluid element and give it a velocity U, but how can we determine what U should be?
Is it wrong to say that the velocity...
Good day,
In my book, the following definition for flow velocity is given:
So summarized, the flow velocity at a point in space is the velocity of an infinitesimally small fluid element as it sweeps through that point. But now my question; how is the velocity of an infinitesimally small...
1. Homework Statement
Consider the following implicit scheme:
y_{n+1}=y_{n}+\frac{\Delta t}{2}\left [f(y_{n+1})+f(y_{n})]
By linearization one can obtain an explicit scheme which is an approximation to this - with approximation error O(\Delta t^{3})
2. Homework Equations
The solution...
Good day,
I don't understand the following:
\frac{d^{2}}{dt^{2}}\int_{0}^{t}(t-\epsilon )\phi (\epsilon)d\epsilon=\phi''(t)
All I know is:
\frac{d^{2}}{dt^{2}}\int_{0}^{t}(t-\epsilon )\phi (\epsilon)d\epsilon=\frac{d^{2}}{dt^{2}}\int_{0}^{t}t \cdot \phi...
1. Homework Statement
Take the Inverse Laplace Transform of: Y(s)=\frac{1}{\tau s+1}\cdot \frac{1}{s}
2. The attempt at a solution
I know:
L^{-1}(\frac{1}{\tau s+1})=\frac{1}{\tau}e^{\frac{-t}{\tau}}
and:
L^{-1}({\frac{1}{s}})=1
But how to continue?