
Let X be a continuous random variable. Prove that: P(21-; < X < xạ) = 1 - a.
let a,b > 0 . Prove that
DI < Val
3.4. Suppose a and b are positive integers. Prove that, if aſb, then a < b.
Let A be an mx n matrix and B be an n xp matrix. (a) Prove that rank(AB) S rank(A). (b) Prove that rank(AB) < rank(B).
Prove
AB _ BC__ AC aven. DEEF DE Prove: <A><D
1. Let x, a € R. Prove that if a <a, then -a < x <a.
Please use induction to prove the following question for all
natural numbers n.
(d) Prove that vns įt<2vn.
Prove that B = {(a,b) x (c,d) | a,b,c,d EQ, a<b, c<d} is a basis for some topology on R2.
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
One characteristic measured about high schools is the percent
free lunch, which is the percentage of the student body that is
eligible for free and reduced-price lunches. The top 100 schools,
grouped according to their percent free lunch, is as follows.
Percent free
lunch (x)
Number of top
100
ranked high schools
46
20
12
10
12
If stratified random sampling with proportional allocation is
used to select a sample of 25 high schools, how many would be
selected...