Prove that if a symmetric matrix is invertible, then its inverse is symmetric also

Week 6 10/3 Section 4.3 continued Binomial Experiment review 1. N trials 2. each trial has 2 outcomes (success and failure) 3. p=success and q=p-q=failure 4. trails are independent - x=number of successes - x=0,1, 2,…n where n is the number of trials n x n-x - p(x) = ( )xp )(q ) because we can’t use calculator we will use table on exam Theorem: if X is binomial, the expected value of: - E(X) = Σx*p(x)= np - V(X)= Σ(x-u) p(x) = npq - Indicator function is only for binomial random variables o X=x +x 1+x 2 n o x= jth indicator function o E(x)=1jp + 0*q = p o V(x)= 1 *p + 0 *q – p 2 j  =p-p= p(1-p)  =pq - in a binomial experiment, the indicator functions are independent, therefore the variance of the sum is the sum of the variances o V(X)= V(x ) +1V(x )…+V2x ) n  =pq + pq…+pq o Standard deviation = square root of npq Example: suppose 40% of New Orleans residents are registered voters; if we obtain a sample of 50 residents, what is the expected number of registered voters - 2 paths: registered or not registers - success: p: registered - failure: q: not registered - n=50 - E(X)= 50(.4)= 20 - V(X)= 50(.4)(.60)=12 Section 4.4 Hypergeometric ONLY: sampling without replacement (similar to a binomial experiment except it fails the 4 condition– the events of success will not be independent) Ex: Urn problem w