1.) Prove that P(n,0)=C(n,0)
2.) Discuss the differences, both in applications and in the formulas, for combinations and permutations. Give an example of each.
1.) Prove that P(n,0)=C(n,0) 2.) Discuss the differences, both in applications and in the formulas, for...
(n) 6. Let X ~ Binomial (n,p). Prove that a. Ex=0 (6)p*(1 – p)n-* = ... = 1 b. E[X] = 21-0 x()p*(1 - 2)^-^ = = mp c. Var[X] = x=0x2 (1)p*(1 – p)n-x – (np)2 = ... = np(1 – p) d. My(t) = ... = (pet + 1 - p)n
+o0 P(A,) 0(n N4 0, 2. Let A A = Q , prove i1 +o0 P(A,) 0(n N4 0, 2. Let A A = Q , prove i1
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
1. Prove that the proposition P(0) is true, where P(n) is “if n > 1, then n? > n" and the domain consists of all integers
Prove that 1-[p(1-p)^0+p(1-p)^1+p(1-p)^2+p(1-p)^3...+p(1-p)^n]=(1-p)^n using geometric series equation.
(2) Define the set A C 2 by s) n-0 (a) Prove that for any N 2 0 the set is compact. (b) Prove that for any є > 0 there exists some N > 0 so that for any x E A we have (c) Prove that A is totally bounded. (d) Prove that A is compact (2) Define the set A C 2 by s) n-0 (a) Prove that for any N 2 0 the set is compact....
Comparing UNIX environments: differences between kernels differences between shells differences between applications 1. You found differences in the way variables must be assigned. These reflect differences between: a. kernels b. shells c. applications 2. You found differences in the way underlying hardware information was returned. These reflect differences between: a. kernels b. shells c. applications 3. You found differences in where log messages are sent for storage. These reflect differences between: a. kernels b. shells c. applications 4. You found...
prove n^3 >=(n+1)^2 for all n>=2 Step by step answer would be appreciated. Prove that the following statement is true oo give counter example, h3> (htig for all nya
1. Justification of the two formulas for permutation and combinations. (15 pts) a) Assume there are n different objects and we want to place them in k different places. By drawing and simplifying, justify that there are P(n,k) ways. P b) Now assume that places are indistinguishable. Use item a to show then answer is C(n,k) as it follows. Explain your answer why do we have to divide by k!. ( n! kn ethe binomial theorem: (a + b)" =...
Problem 1. Let A be an m x m matrix. (a) Prove by induction that if A is invertible, then for every n N, An is invertible. (b) Prove that if there exists n N such that An is invertible, then A is invertible. (c) Let Ai, . . . , An be m x m matrices. Prove that if the product Ai … An is an invertible matrix, then Ak is invertible for each 1 < k< n. (d)...