Exercise: time until consecutive successes 3 points possible (ungraded) consider a sequence, x, of independent bernoulli random variables with common success probability p 1/4. let t be the first time at which we have a success immediately following a previous success; that is, t = min{n : xn = xn-1 = success). we are interested in ein we model this problem using the following markov chain 3/4 1/4 4 f ss1 1/4 the state s denotes a success, state f denotes a failure, and state ss is an absorbing state denoting the event that we have obtained two successes in a row. calculate the numerical values of the following quantities 1. 2. 3.

Afamily has two cars. the first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. during one particular week, the two cars went a combined total of 1025 miles, for a total gas consumption of 55 gallons. how many gallons were consumed by each of the two cars that week?

The temperature of a chemical solution is originally 21 ? c . a chemist heats the solution at a constant rate, and the temperature of the solution 75 ? c after 1212 12 minutes of heating. the temperature, tt t , of the solution in ? c is a function of x , the heating time in minutes. write the function's formula.

Lab 1: central tendency and standard deviation directions: use excel to compute descriptive statistics. problem: you are the manger of a fast food store. part of your job is to report to the boss at the end of each day which special is selling best. use your knowledge of descriptive statistics and write one paragraph to let the boss know what happened today. here are the data. use excel to compute important values (mean, median, mode, and standard deviation). make sure to include a copy of your work. this should be submitted via canvas (no exceptions). make sure you include your excel work in addition to a summary of the results. special number sold cost huge burger 20 $2.95 baby burger 18 $1.49 chicken littles 25 $3.50 porker burger 19 $2.95 yummy burger 17 $1.99 coney dog 20 $1.99 total specials sold 119