Nick and penny are independently performing independent bernoulli trials. for concreteness, assume that nick is ipping a nickel with probability p1 of heads and penny is ipping a penny with probability p2 of heads. let x1; x2; : : : be nick's results and y1; y2; : : : be penny's results, with xi bern(p1) and yj bern(p2). (a) find the distribution and expected value of the rst time at which they are simultaneously successful, i. e., the smallest n such that xn = yn = 1. hint: de ne a new sequence of bernoulli trials and use the story of the geometric. (b) find the expected time until at least one has a success (including the success). hint: de ne a new sequence of bernoulli trials and use the story of the geometric

At river bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge. calculate the income earned in one month on the checking account for a customer with an account balance of $1,000. a. $4.25 b. $5.50 c. $6.75 d. $7.25 checking account earnings at baker’s bank are expressed by the equation: i = -0.09x + 10.2. while the earnings at elite bank are modeled by: i = -0.02x + 7.5. in both cases, x is the number of checks written. at what number of checks will elite bank start generating more checking account income than baker's bank? a. 12 b. 25 c. 39 d. 42 emilio’s checking account had a balance of 728.32 at the beginning of the week. he wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. he also deposited his paycheck in the amount of $1,109.90. what is his account balance at the end of the week? a. $1,192.35 b. $1,222.86 c. $1,540.52 d. $1,614.96