Recent content by umzung

So I get $$ \frac {3}{8} s + \frac {3}{8} s^2+...+ \frac {3}{8} s^6$$ and it's a geometric distribution, range 1 to 6?

(a) I find the geometric distribution $$X~G0(3/8)$$ and I find p to be 0.375 since the mean 0.6 = p/q. So p.g.f of X is $$(5/8)/(1-(3s/8))$$. (b) Not sure how to find the p.g.f of Y once we know there are 6 customers?

Got it, thanks.

$$p$$ is the probability, $$q$$ is (1 - probability) and $$s$$ is a dummy variable, not a random variable.

I know the p.g.f. of X is $$q/(1-ps)$$ and that the mean is $$p/q$$, but how do I find a specific value for p here?

That's clearer, thanks.

How does become ? I can see the s has been factored out and the power of 6 distributed, but how do we know this happens, short of multiplying out the brackets?

Thanks. The formula is first term*(1-r^n)/(1-r). How does 1-r become reversed in the solution?

I'm using the sum of a geometric series formula, but I'm not sure how to find the ratio, r. The n is confusing me. The solution is below, but I'm having trouble with the penultimate step.

I think I have it now. The key to the answer is that $$10\pi=((10\pi)^{3/2})^{2/3}$$ which I can then bring inside the brackets.

$$10π \left( \frac V {4π} \right)^{2/3} = 5\sqrt[3] {{V^2}\frac π 2}$$Not sure how to deal with the $$10π$$ and how we get $$\frac π 2$$.

The full problem statement is as follows: The suspension of a modified baby bouncer is modeled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modeled by a second model spring PC with stiffness k2...

Homework Statement The suspension of a modified baby bouncer is modeled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modeled by a second model spring PC with stiffness k2. The bouncer is...

Ker(ϕ2) = {z is in C: ϕ(z) = 0} = {z is in C: z* (complex conjugate) + iz = 0} = {z is in C: z* = -iz. Im(ϕ2) = the set of complex numbers. Not sure if that makes sense. Ker(ϕ3) = {z is in C*: ϕ(z) = 1} = {z is in C*: (z* (complex conjugate))^2 = 1}...

Homework Statement Are these functions homomorphisms, determine the kernel and image, and identify the quotient group up to isomorphism? C^∗ is the group of non-zero complex numbers under multiplication, and C is the group of all complex numbers under addition. Homework Equations φ1 : C−→C...