Consider a sequence of n+1 independent tosses of a biased coin, at times k=0,1,2,…,n . On each toss, the probability of Heads is p , and the probability of Tails is 1−p . A reward of one unit is given at time k , for k∈{1,2,…,n} , if the toss at time k resulted in Tails and the toss at time k−1 resulted in Heads. Otherwise, no reward is given at time k . Let R be the sum of the rewards collected at times 1,2,…,n . We will find E[R] and Var(R) by carrying out a sequence of steps. Express your answers below in terms of p and/or n using standard notation (available through the "STANDARD NOTATION" button below.) Remember to write "*" for all multiplications and to include parentheses where necessary. We first work towards finding E[R] . 1. Let Ik denote the reward (possibly 0) given at time k , for k∈{1,2,…,n} . Find E[Ik] . E[Ik]= unanswered

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

the final price would be 29.6925

step-by-step explanation:

39.59 minus 25% equals 29.6925

ur mom

step-by-step explanation: