(2 pts) Verify that for j > 1: P(Bin(n, p) = j) * P(Bin(n,p) =– 1)...
Problem 44) Prove: n!> 2" for n24. Problem 45) Prove by induction: For n>0·AT- i=1
For some n > 1, let T E End(Pn) be given by T(p) = p'. Show that T is not diagonalizable.
3. (10 pts.) X is a Gaussian random variable with E{X} = 2 and Var(X) = 16. Let Y = 3X +1. Determine the probability: Pr(Y > 2)
Let a1 = 3 and an+1 = a + 5 2an for all n > 1 Prove that (an)nen converges and find limn7oo an:
2. Let YBinomial (n, p) where p docs not depend on . Without using the WLLN (but you can use e.g. Chebychev's inequality) show that (a) Y/n-, p as n → oo (b) (1-Y/n)-> (1-p) as n → oo
Question 2 7 pts Theorem If A1, A2, .., A, are sets for n > 2, then (A, UA, U... A.) = (A) n(A)n... n(A) Upload Choose a File Question 3 6 pts o el DLL
1. The probability mass function of a random variable X is given by Px(n) bv P Yn (a) Find c (Hint: use the relationship that Σο=0 (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3) n-0 n! ex)
#include<stdio.h> eint main() { int i = 0, j = 0; while (i < 10|| j < 7) { i++; j++; } printf("%d, %d\n", i, j); getchar(); return 0; } 01,01 10,10 7.7 10,7
1. Assume X is Binomial (n, p), where the constant p (0,1) and the integer n > 0. (a) Express PX > 0) in terms of n and p (b) Define Y = n-X. Specify the distribution of Y.
(5) Use induction to show that Ig(n) <n for all n > 1.