Homework Statement
Say X and Y are independent random variables with densities f and g, respectively:
f(x) = e^(-x) if x > 0 and 0 if x < 0
g(y) = 2e^(-2y) if y > 0 and 0 if y < 0
Calculate a density function for Y/(X+1)
Homework Equations
Change of variable?
Convolution...
Homework Statement
Say X has a density f(x) = 3x^(-4) if x > 1, and 0 otherwise. Now say X1,...,X16 are independent with density f. Let Y = (X1X2...X16)^(1/16). Find E(Y) and Var(Y).
Homework Equations
Var(Z) = E(Z^2) - [E(Z)]^2
E(Z) = Integral from -inf to +inf of z*f(z)dz
The...
Thank you so much pgraves013! That makes so much sense!
Do you know how to find the initial acceleration of mass M1 just after the masses are released? (there is no external force during that part)
A friend of mine gave me this problem, and it was somewhat hard:
A rectangular block of mass M1 rests on a horizontal table. Masses M2 and M3 are free to slide along the surfaces of M1 and are attached by a massless string over a frictionless pulley.
For the diagram, go to...
Ahhh Doc Al, thank you very much. I just edited my post right before you posted that, and you confirmed my prediction.
I appreciate everyone's help a lot. This problem has been bugging me so much. It's nice to have some closure. =)
So does this mean if w and v were velocities, and not...
I don't understand - if its going at speed v -w and bounces back at speed v -w (relative to the big object at rest), where does the term v+ 2w come from (assuming the big object has speed w)?Edit: Hm, for some reason, I think the v + 2w answer comes up only when you use the word SPEED...
This is exactly how I thought it would be as well. However, I was doing a problem about a bullet traveling to the right at velocity v1 towards a block of wood attached to a pendulum. The pendulum was at the lowest point of the swing when the two elastically collided (so essentially, the block...
Why is it that when a small object traveling at velocity v, when colliding with a much larger object traveling at velocity w, ends up with a final velocity of 2w + v? What happens to the velocity of the large object?
I have seen the math behind this, but conceptually, I don't see how this...
James Joule is credited with the first law.
Sadi Carnot is considered the Father of Thermodynamics. You may know of him from the Carnot heat engine and the Carnot cycle (from which follows the second law of thermodynamics).
Also, do you know the concept of Impulse? It has the same dimensions of momentum, but is more precisely defined as a Force acting over a certain amount of time. That's why when you drop an egg on a pillow, it will not break, but when you drop an egg on concrete, it will. Because the egg has some...
The radius vector \vec{r} is the vector from some origin to the position of the particle at some time t. Typically, \vec{r}(t) is the trajectory, so to speak of the particle, so the derivative with respect to time is the velocity: v_t = \frac{d\vec{r}}{dt}. Because the position is constantly...
Ack! I am terribly sorry - I made a sign error when I added 3 and -5. You are correct! I edited the post with the necessary changes.
You are also correct when you say "he force is in negative horizontal or vertical
direction, arent we suppose to assume the direction of acceleration also negative...