A monkey randomly hits a keyboard with 26 letters, one per second. (a) How long, in...

A monkey randomly hits a keyboard with 26 letters, one per second.

(a) How long, in average, will it take for the monkey to type the letter Z for the first time?

I believe that each letter is random and independent, meaning that the probability of the monkey typing any letter is (1/26). Therefore, the expected value is equal to the sum from 1 to 26 times (1/26), yielding 13.5 seconds. I am unsure how to move forward with parts (b) and (c).

(b) How long, in average, will it take for the monkey to type the letter Z for the second time?

(c) How long, in average, will it take until the monkey types two Z’s in a row? (Hint: condition on the event that the Monkey types Z on the first second).

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A seqstring is a sequence of 18 letters(one of the 26 lowercase letters a-z). How many...

A seqstring is a sequence of 18 letters(one of the 26 lowercase letters a-z). How many seq strings are there where the number of letters between any two occurences of the same letter is at least 2?

Nagle algorithm Suppose a transmitter application wants to send the letters "abcdefghi", one letter per second....

Nagle algorithm Suppose a transmitter application wants to send the letters "abcdefghi", one letter per second. The transmitter uses a TCP connection with an RTT of 4.3 seconds. Assuming the use of Nagle's algorithm, show, using a table, the time of sending and the contents of each packet sent.

1. How many permutations of the 26 letters are there that contain none of the sequences...

1. How many permutations of the 26 letters are there that contain none of the sequences ROCK, STONE, PLUG, FIT or HAY?

If you can read at an average rate of 5.15 words per second, how long will...

If you can read at an average rate of 5.15 words per second, how long will it take you to read a 505 page book that has an average of 995 words per page? Let’s say you need to make 12.0 dozen cookies. You decide to make these cookies in batches of 24.0 cookies each. Each batch of cookies requires 27.0 mL of vanilla extract. Each bottle of vanilla extract contains 150. mL of liquid. How many bottles of vanilla...

--A software company uniformly randomly generates 14-character encryption keys from 26 letters and 10 digits. Repeated...

--A software company uniformly randomly generates 14-character encryption keys from 26 letters and 10 digits. Repeated characters are allowed, and the order of the characters matters. (a) How many different keys can be generated, if there are no restrictions at all on the keys? (b) What is the probability that a key consists of only letters? (c) What is the probability that a key starts and ends with a digit? (d) If the digits are removed from the 14-character key...

How do letters of credit and drafts work together? How does this create one of the...

How do letters of credit and drafts work together? How does this create one of the most liquid money market instrument?

Your computer manufacturing firm must purchase 12,000 keyboards from a supplier. One supplier demands a payment of $144,000 today plus $12 per keyboard payable in one year. Another supplier will charge $25 per keyboard, also payable in one year. The ri

Your computer manufacturing firm must purchase 12,000 keyboards from a supplier. One supplier demands a payment of $144,000 today plus $12 per keyboard payable in one year. Another supplier will charge $25 per keyboard, also payable in one year. The risk-free interest rate is 9%. a. What is the difference in their offers in terms of dollars today? Which offer should your firm take? b. Suppose your firm does not want to spend cash today. How can it take the first offer...

One long wire carries current 16.0 A to the left along the x axis. A second...

One long wire carries current 16.0 A to the left along the x axis. A second long wire carries current 72.0 A to the right along the line (y = 0.280 m, z = 0). (a) Where in the plane of the two wires is the total magnetic field equal to zero? (b) A particle with a charge of ?2.00 µC is moving with a velocity of 150î Mm/s along the line (y = 0.100 m, z = 0). Calculate...

One long wire carries current 32.0 A to the left along the x axis. A second...

One long wire carries current 32.0 A to the left along the x axis. A second long wire carries current 68.0 A to the right along the line (y = 0.280 m, z = 0). a) (5 points) Where in the plane of the two wires is the total magnetic field equal to zero? b) (5 points) A particle with a charge of −2.00 µC is moving with a velocity of 150 î Mm/s along the line (y = 0.100...

One long wire carries current 12.0 A to the left along the x axis. A second...

One long wire carries current 12.0 A to the left along the x axis. A second long wire carries current 80.0 A to the right along the line (y = 0.280 m, z = 0). (a) Where in the plane of the two wires is the total magnetic field equal to zero? y = ________m (b) A particle with a charge of −2.00 µC is moving with a velocity of 150î Mm/s along the line (y = 0.100 m, z...

Subjects