probability

Consider n independent rolls of a k-sided fair die with k≥2: the sides of the die are labelled 1,2,…,k and each side has probability 1/k of facing up after a roll. Let the random variable Xi denote the number of rolls that result in side i facing up. Thus, the random vector (X1,…,Xk) has a multinomial distribution.

1. Which of the following statements is correct? Try to answer without doing any calculations.

- unanswered X1 and X2 are uncorrelated.X1 and X2 are positively correlated.X1 and X2 are negatively correlated.
2. Find the covariance, cov(X1,X2), of X1 and X2. Express your answer as a function of n and k using standard notation. Hint: Use indicator variables to encode the result of each roll.

cov(X1,X2)= - unanswered
3. Suppose now that the die is biased, with a probability pi≠0 that the result of any given die roll is i, for i=1,2,…,k. We still consider n independent tosses of this biased die and define Xi to be the number of rolls that result in side i facing up.

Generalize your answer to part 2: Find cov(X1,X2) for this case of a biased die. Express your answer as a function of n,k,p1,p2 using standard notation. Write p1 and p2 as 'p_1' and 'p_2', respectively, and wrap them in parentheses in your answer; i.e., enter '(p_1)' and '(p_2)'.

cov(X1,X2)= - unanswered

  1. 👍
  2. 👎
  3. 👁
  1. 1. x1 x2 are negative correlated
    2. covariance is : -n/(k^2)
    3. unaswered (if anyone please post)!

    1. 👍
    2. 👎
  2. 3. -n*(p_1)*(p_2)

    by the book solution. Instead of p_i or p_j we are given p_1 and p_2. In any case, k is useless

    hi there Juan Pro and Anonymous...First and foremost if you are able to provide the answers to the rest of this problem set....you are more than welcome

    Thanks for providing the answers to questions 1 and 2

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Statistics

    you roll two fair dice, a green one and a red one? (a) are the outcomes on the dice independent? (b)Find P(1 on green die and 2 on red die) (c)Find P(2 on green die and 1 on red die) (d)Find P(1 on green die and 2 on red die) or

  2. Math

    Maria has an 8-sided die that is numbered from 1 to 8. She rolls the die 96 times. About how many times can she expect to roll an 8?

  3. math

    A six-sided die with sides numbered 1 through 6 is tossed twice. What is the probability of getting a number larger than 4 on both throws

  4. math

    A red die and a green die have been rolled. (6 sided) What is the probability of the event? 1.The number on the red die is greater than the number on the green die (Answer is 5/12 but how?) 2. The sum is less than 10. 3. The sum

  1. Probability

    You roll two five-sided dice. The sides of each die are numbered from 1 to 5. The dice are “fair" (all sides are equally likely), and the two die rolls are independent. Part (a): Event A is “the total is 10" (i.e., the sum of

  2. algebra

    you flip a coin and then roll a fair six-sided die.what is the probability the coin lands heads and the die shows a one.

  3. Probability

    Consider an experiment in which a fair four-sided die (with faces labeled 0 , 1 , 2 , 3 ) is rolled once to determine how many times a six-sided die (with faces labeled 1 ,.., 6 ) is rolled. The die rolls are independent. Let X be

  4. math

    What is the probability of rolling a 5 on a 6-sided die? I believe this is 1/6 because there is only one 5 on a 6-sided die. I am stuck on this part of the question: If you roll the die 6 times, how many 5’s do you expect to

  1. probability and statistics

    Roll a fair six-sided die until you roll a number that is less than one of your previous rolls. To three decimal places, what is the expected value of the number of rolls made?

  2. math

    A six-sided die (with numbers 1 through 6) and an eight-sided die (with numbers 1 through 8) are rolled. What is the probability that there is exactly one 6 showing? Express your answer as a common fraction.

  3. Probability

    The newest invention of the 6.041x staff is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. Consider a sequence of six independent rolls of this

  4. **************HELP STATISTIC PLEASE*************

    NEED SOMEONE TO RECHECK ANS *****HELP PLEASE HAS STAR BY MY ANSWER If P (A) = 0.2 and P (B) = 0.3 and A and B are disjoint, what is P (A or B)? (1 point) 0.00 0.06 0.10 0.44 *0.50 4. Given that you roll a fair six-sided die, what

You can view more similar questions or ask a new question.