(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?
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?
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.
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...