Recent content by slipperypete

Suppose you have multiple independent Bernoulli random variables, X_1,X_2,...,X_n, with respective probabilities of success p_1,p_2,...,p_n. So E(X_i)=p_i, and E(X_i+X_j)=E(X_i)+E(X_j). Also, \text{var}(X_i)=p\cdot (1-p), and \text{var}(X_i+X_j)=\text{var}(X_i)+\text{var}(X_j). (Though...

Let X be the set X=\left\{x_1,x_2,...,x_n\right\}, where each x_i is a Bernoulli random variable and P be the set P=\left\{p_1,p_2,...,p_n\right\}, where p_i is the probability that x_i=1. Now, suppose there are two other sets, A=\left\{a_1,a_2,...,a_n\right\} and...

I started my way through baby Rudin recently, been able to answer every question so far, but I just can't get #16 from Chapter 1. I (think) understand the geometry of it perfectly. I just can't prove it rigorously/analytically. I haven't been able to do anything for 3 days now, except think...