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...