Given ?(?) = sqrt(3 + ? ) + 4. Use the definition of 4.4.3 to
evaluate each of the area in the range [0, 6] if ? = 4.
a) Find the area under the curve when ?? ∗ is the left endpoint
of the subinterval.
b) Find the area under the curve when ?? ∗ is the midpoints of
the subinterval.
c) Find the area under the curve when ?? ∗ is the right endpoint
of the subinterval.
Let G = Z4 × Z4, H = ⟨([2]4, [3]4)⟩.
(a) Find a,b,c,d∈G so that G is the disjoint union of the 4
cosets a+H,b+
H, c + H, d + H. List the elements of each coset.
(b) Is G/H cyclic?
1) The PDF of a Gaussian random variable is given by fx(x).
fx(x)= (1/(3*sqrt(2pi)
)*e^((x-4)^2)/18
determine
a.) P(X > 4) b). P(X > 0). c). P(X
< -2).
2) The joint PDF of random variables
X and Y is given by
fxy(x,y)=Ke^-(x+y), x>0 , y>0
Determine
a. The constant k.
b. The marginal PDF fX(x).
c. The marginal PDF fY(y).
d. The conditional PDF fX|Y(x|y). Note
fX|Y(x|y) =
fxy(x,y)/fY(y)
e. Are X
and Y independent.
Use f(x) = ?2x, g(x) = square root of x and h(x) = |x| to find
and simplify expressions for the following functions and state the
domain of each using interval notation. a . (h ? g ? f)(x) b. (h ?
f ? g)(x) (g ? f ? h)(x)