Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t.
(a) Find a...
Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t.
(a) Find a system of two equations in four unknowns whose
solution set is spanned by X and Y.
(b) Find a system of three equations in four unknowns whose
solution set is spanned by X and Y.
(c) Find a system of four equations in four unknowns that has
the set of vectors of the form Z + aX + bY as its general solution
where Z = [1, 1, 1, 1]t.
Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y
<= 1, 2*y <= x. (And 0 otherwise)
Let the random variable W = X + Y.
Without knowing the p.d.f of W, what interval of w values holds
at least 60% of the probability?
1) Find y as a function of t if 9y′′+24y′+32y=0,
y(0)=5,y′(0)=8. y(t)=
2) Find y as a function of x if y′′′+16y′=0,
y(0)=−5, y′(0)=−32, y′′(0)=−32. y(x)=
3) Find y as a function of t if 9y′′−12y′+40y=0,
y(1)=5,y′(1)=9. y=
Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and
0<=y<=1.
a) Find k.
b) Find the joint cumulative density function of (X,Y)
c) Find the marginal pdf of X and Y.
d) Find Pr[Y<X2] and Pr[X+Y>0.5]
1.Evaluate the integral C where C is x=t^3 and y=t, 0 ≤ t ≤
1
2.Find the area of the surface with vectorial equation
r(u,v)=<u,u sinv, cu >, 0 ≤ u ≤ h, 0≤ v ≤ 2pi