Suppose that x1, x2 and x3 are independent bernoulli random variables, each has expected value 2/3. • define x = x1 + x2 + x3. what is the expected value of x? what is the variance? • define y = 3x1. what is the expected value of y ? what is the variance? • is x a binomial random variable? • is y a binomial random variable? • calculate p(x = y ).

Suppose you want to transform the graph of the function y=tan(x+pi/4)-1 into the graph of the function y=-tan(x+pi/2)+1 which transformations should you perform. a) reflect the graph of the first function across the x-axis, translate it pi/4 units to the left, and translate it 2 units up. b) reflect the graph of the first function across the x-axis, translate it pi/4 units to the right, and translate it 2 units up. c) reflect the graph of the first function across the line y = -1, translate it pi/4 units to the left, and translate it 2 units up. d) reflect the graph of the first function across the line y = -1, translate it pi/4 units to the right, and translate it 2 units up.