Let x be a discrete random variable that takes on the values i æ 0, 1, 2, . . with probability mass function (pmf): p(x æ i ) æ c ¸i i ! (1) where ¸ è 0 is a fixed and known positive number and c is a (yet to be determined) real number. (a) find the value of c which makes p(x æ i ) a valid probability function. remember we need the probability of all outcomes to be equal to 1. or more specifically: 1 æ 1x iæ0 p(x æ i ). (b) determine p(x æ 0) (c) determine p(x è 2). hint: it might be to use the law of total probability which tell us that 1 æ p(x · 2)åp(x è 2).

You earn a 12% commission for every car you sell. how much is your commission if you sell a $23,000 car?

Tim has obtained a 3/27 balloon mortgage. after the initial period, he decided to refinance the balloon payment with a new 30-year mortgage. how many years will he be paying for his mortgage in total?

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.