E(Y) = 4, E(X) = E(Y+2), Var(X) = 5, Var(Y) = Var(2X+2)
a. What is E(2X -2Y)?
b. What is Var(2X-Y+2)?
c. What is SD(3Y-3X)?
2)
In a large community, 65% of the residents want to host an
autumn community fair.
The rest of the residents answer either disagree or no opinion
on this proposal.
A sample of 18 residents was randomly chosen and asked for their
opinions.
a) What is th probability that the residents answer either
disagree or...
Consider the ODE y"+ 4 y'+ 4 y = 5 e^(− 2 x ). (
a) Verify that y 1 ( x) = e − 2 x and y 2 ( x) = xe − 2 x
satisfy the corresponding homogeneous equation.
(b) Use the Superposition Principle, with appropriate
coefficients, to state the general solution y h ( x ) of the
corresponding homogeneous equation.
(c) Verify that y p ( x) = 52 x 2 e − 2 x...
Consider the region bounded between y = 3 + 2x - x^2 and y = e^x
+ 2 . Include a sketch of the region (labeling key points) and use
it to set up an integral that will give you the volume of the solid
of revolution that is obtained by revolving the shaded region
around the x-axis, using the... (a) Washer Method (b) Shell Method
(c) Choose the integral that would be simplest to integrate by hand
and integrate...
If G = (V, E) is a graph and x ∈ V , let G \ x be the graph
whose vertex set is V \ {x} and whose edges are those edges of G
that don’t contain x.
Show that every connected finite graph G = (V, E) with at least
two vertices has at least two vertices x1, x2 ∈ V such that G \ xi
is connected.