probability

Let X be a continuous random variable. We know that it takes values between 0 and 3, but we do not know its distribution or its mean and variance. We are interested in estimating the mean of X, which we denote by h. We will use 1.5 as a conservative value (upper bound) for the standard deviation of X. To estimate h, we take n i.i.d. samples X1,X2,…,Xn, which all have the same distribution as X, and compute the sample mean

H=1n∑i=1nXi.
Express your answers for this part in terms of h and n using standard notation.

E[H]=- unanswered
Given the available information, the smallest upper bound for var(H) is: - unanswered
Calculate the smallest possible positive value of n such that the standard deviation of H is guaranteed to be at most 0.01.

This minimum value of n is: - unanswered
We would like to be at least 99% sure that our estimate is within 0.05 of the true mean h. Using the Chebyshev inequality, calculate the minimum value of n that will achieve this.

This minimum value of n is: - unanswered
Assume that X is uniformly distributed on [0,3]. Using the Central Limit Theorem, identify the most appropriate expression for a 95% confidence interval for h.

- unanswered [H−1.96n−−√,H+1.96n−−√] [H−1.96⋅3−−−−−−√4n−−√,H+1.96⋅3−−−−−−√4n−−√] [H−1.963√4n−−√,H+1.963√4n−−√] [H−1.96⋅34n−−√,H+1.96⋅34n−−√

  1. 👍 0
  2. 👎 0
  3. 👁 511
  1. 5. H-1.96*(3^0.5)/((4*n)^0.5),
    H+1.96*(3^0.5)/((4*n)^0.5)

    1. 👍 0
    2. 👎 0
  2. does someone have an answer for this question? i am stuck

    1. 👍 0
    2. 👎 0
  3. please provide answer . anyone here to provide help

    1. 👍 0
    2. 👎 0
  4. Help is much appreciated, please!

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. statistics

    The random variable W can take on the values of 0, 1, 2, 3, or 4. The expected value of W is 2.8. Which of the following is the best interpretation of the expected value of random variable W? A. A randomly selected value of W must

  2. probability; math

    Let X be a continuous random variable. We know that it takes values between 0 and 6 , but we do not know its distribution or its mean and variance, although we know that its variance is at most 4 . We are interested in estimating

  3. statistics

    Suppose that the random variable Θ takes values in the interval [0,1]. a) Is it true that the LMS estimator is guaranteed to take values only in the interval [0,1]? b) Is it true that the LLMS estimator is guaranteed to take

  4. Mathematics

    Let Z be a nonnegative random variable that satisfies E[Z4]=4 . Apply the Markov inequality to the random variable Z4 to find the tightest possible (given the available information) upper bound on P(Z≥2) . P(Z≥2)≤

  1. Probability

    Let Z be a nonnegative random variable that satisfies E[Z^4]=4. Apply the Markov inequality to the random variable Z^4 to find the tightest possible (given the available information) upper bound on P(Z≥2). P(Z>=2)

  2. Probability

    Question:A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, then K=5. For K=1,2,3...K,

  3. math

    Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ (lambda) = 0.5. What's the probability that a repair takes less than 5 hours? AND what's the

  4. math 115

    Let x be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation 25. Find the value of x so that the area under the normal curve between ì and x is approximately 0.4798 and the

  1. probability

    A fair coin is flipped independently until the first Heads is observed. Let K be the number of Tails observed before the first Heads (note that K is a random variable). For k=0,1,2,…,K, let Xk be a continuous random variable

  2. probability

    t the discrete random variable X be uniform on {0,1,2} and let the discrete random variable Y be uniform on {3,4}. Assume that X and Y are independent. Find the PMF of X+Y using convolution. Determine the values of the constants

  3. probability

    The random variable X has a PDF of the form fX(x)={1x2,0,for x≥1,otherwise. Let Y=X2 . For y≥1 , the PDF of Y it takes the form fY(y)=ayb . Find the values of a and b . a= b=

  4. Probability

    The sample mean Let X be a continuous random variable. We know that it takes values between 0 and 6, but we do not know its distribution or its mean and variance, although we know that its variance is at most 4. We are interested

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