stats again please help

posted by .

When a computerized generator is used to generate random digits, the proability that any particular digit in the set {0,1,2, . . .,9} is generated on any individual trial is 1/10-0.1. suppose that we are generating digits one at a time and are interested in tracking occurrences of the digit 0.

Determine the probabiliy that the first 0 occurs as the fifth random digit generated?

so the probability of not getting a zero for the first four time is 9/10. then the probability of getting a zero for the fifth time is 1/10. and i just multiply that right.

****how many digits would you expect to have to generate in order to observe the first o.

please help me. am i doing this right?

The probability of generating a zero is 1/10, so you would expect to have to generate 10 digits.

You can calculate this from the defintion of the expectation value with a bit of brute force as follows:

The probability that the n-th random digit is the first zero is:

P(n) = (9/10)^(n-1) * 1/10

The expectation value for n is:

<n> = sum_{n=1}^{infinity} n*P(n)

You can calculate this summation using the formula for the geometric series:

sum_{n=0}^{infinity} x^n = 1/[1-x]

differentiate both sides w.r.t. x:

sum_{n=1}^{infinity} nx^(n-1) =
1/[1-x]^(2)

Note that the lower limit of the summation changes to n = 1 because the n = 0 term is a constant which vanishes when differentiated.


Inserting x = 9/10 in here and multiplying by 1/10 gives:

<n> = 1/10 * 1/[1/10]^2 = 10

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    using digits 1-9 only once, multiply a 3 digit by a 2 digit number and get a 4 digit result 12*345=4140?
  2. stats please help test tom

    When a computerized generator is used to generate random digits, the proability that any particular digit in the set {0,1,2, . . .,9} is generated on any individual trial is 1/10-0.1. suppose that we are generating digits one at a …
  3. Math Help Please

    Would you please explain the steps you used to get the answer 2469. Thank you Using the 9 digits, 1, 2, 3, 4, 5, 6,7, 8 and 9 you can arrange four different digits to form a four-digit number that is NOT divisible by 7. The digits …
  4. Math

    Received answer to the following question from Jishka. (2469) Would you please explain the steps you used to get the answer 2469. I must show work. Thank you Using the 9 digits, 1, 2, 3, 4, 5, 6,7, 8 and 9 you can arrange four different …
  5. finite math

    suppose that 3 digits are selected at random from the set S={1,2,3,4,5,6} and are arranged in random order. Find the probability that the resulting 3-digit number is less than 300.
  6. statistics

    A random number generator draws at random with replacement from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. In 5000 draws, the chance that the digit 0 appears fewer than 495 times is closest to 25%,30%,35%,40%,45%,50%
  7. Data Structures and Algorithms

    The "random" numbers produced by computers aren't purely random. They are actually pseudo-random, meaning that they are produced by mathematical formulas that simulate randomness.The linear congruential generator takes a seed X0 and …
  8. Math

    In a table of random digits, each digit is to occur with a probability of 0.1. a) A student examines a list of 200 random digits and counts only eleven 4’s and thus claims that the table is not really random. Explain the error in …
  9. Stats

    Describe how to use a source of random data to simulate multiple trials of this situation. A student guesses on all 10 questions of a multiple-choice quiz. Each question has three choices. a. Assign 00-09 to all of the correct answers …
  10. math

    If a digit can be used more than once, what is the probability that the last two digits of a randomly generated 5-digit number are both 4?

More Similar Questions