1. Identify with the information below whether X is a discrete or continuous random variable.
(a) Let X be the height of a randomly selected 8-year-old child.
(b) Let X be a random values on the nonnegative integers, i.e. X E {0, 1, 2, 3,.... }.
(c) Let X be a random variable that takes values on all nonnegative real numbers, i.e.
X >= 0.
(d) Let X be the number of 8-year-old children who will attend the 1:30 showing of the
movie Epic.
(e) Let X be the number of defective light bulbs in a shipment.
Solution
1.
a- continuous
b- discrete
c-continuous
d-discrete
e-discrete
2..
1. If a 10 10 matrix A has 6 distinct eigenvalues,then what is.pdf
1. 1. If a 10 * 10 matrix A has 6 distinct eigenvalues,
then what is the smallest that the rank of A can be?
2. If T: R3---->R2 is a linear transformation, and T(u)=[1,2] and T(v)=[3,4], then T(5u-v) must
be what vector?
3. True or False? If AB = AC then det(B)=det(C).
4. T or F? If A is a 3*3 matrix and has eigenvalues 1,2 and 5, then A is diagonalizable and det
A=10.
Solution
1)
rank =6.
2) T(5u-v) = 5T(u) - T(v) = [5 10] -[3 4] =[2 6]
3) AB=AC
False
if det(A)=0
then det(B) and det(c) can be anything
4) A = T*D*T^-1
elements of D are eigen values
Det(D) = 5*2*1 =10
det(A) = det(D) =10
![1. If a 10 * 10 matrix A has 6 distinct eigenvalues,
then what is the smallest that the rank of A can be?
2. If T: R3---->R2 is a linear transformation, and T(u)=[1,2] and T(v)=[3,4], then T(5u-v) must
be what vector?
3. True or False? If AB = AC then det(B)=det(C).
4. T or F? If A is a 3*3 matrix and has eigenvalues 1,2 and 5, then A is diagonalizable and det
A=10.
Solution
1)
rank =6.
2) T(5u-v) = 5T(u) - T(v) = [5 10] -[3 4] =[2 6]
3) AB=AC
False
if det(A)=0
then det(B) and det(c) can be anything
4) A = T*D*T^-1
elements of D are eigen values
Det(D) = 5*2*1 =10
det(A) = det(D) =10](https://image.slidesharecdn.com/1-230327161444-2dd3c6ef/85/1-If-a-10-10-matrix-A-has-6-distinct-eigenvalues-then-what-is-pdf-1-320.jpg)
