Question

In: Statistics and Probability

You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly...

You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly distributed in the interval from X to X+7 , where X is an unknown real valued parameter. Derive the ML (maximum likelihood) estimator for X. Given the observations 28.91 , 26.52 , 28.54 , 28.69 , 26.86 , 23.90 , 26.08 , 26.73 , 25.65 , 25.14 , 29.51 , 26.77 , compute the ML estimate for X. If the ML estimate is a range of values, then compute the midpoint of the interval of ML estimates and provide it as your answer.

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly...
You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly distributed in the interval from X to X+10 , where X is an unknown real valued parameter. Derive the ML (maximum likelihood) estimator for X. Given the observations 16.10 , 22.84 , 19.96 , 24.54 , 15.36 , 19.01 , 15.65 , 24.20 , 14.63 , 22.33 , compute the ML estimate for X. If the ML estimate is a range of values, then...
URGENT!! PLEASE ANSWER QUICKLY You are given a number of i.i.d. (independent and identically distributed) observations...
URGENT!! PLEASE ANSWER QUICKLY You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly distributed in the interval from X to X+8 , where X is an unknown real valued parameter. Derive the ML (maximum likelihood) estimator for X. Given the observations 28.93 , 29.29 , 30.95 , 33.68 , 34.29 , 34.01 , 30.24 , 31.96 , 28.41 , 28.58 , 28.78 , 33.12 , 31.65 , compute the ML estimate for X....
Let Z1, Z2, . . . , Zn be independent and identically distributed as standard normal...
Let Z1, Z2, . . . , Zn be independent and identically distributed as standard normal random variables. Prove the distribution of ni=1 Zi2 ∼ χ2n. Thanks!
Let ?1 , ?2 , ... , ?? be independent, identically distributed random variables with p.d.f....
Let ?1 , ?2 , ... , ?? be independent, identically distributed random variables with p.d.f. ?(?) = ???−1, 0 ≤ ? ≤ 1 . c) Show that the maximum likelihood estimator for ? is biased, and find a function of the mle that is unbiased. (Hint: Show that the random variable −ln (??) is exponential, the sum of exponentials is Gamma, and the mean of 1/X for a gamma with parameters ? and ? is 1⁄(?(? − 1)).) d)...
Let X1, X2, . . . be a sequence of independent and identically distributed random variables...
Let X1, X2, . . . be a sequence of independent and identically distributed random variables where the distribution is given by the so-called zero-truncated Poisson distribution with probability mass function; P(X = x) = λx/ (x!(eλ − 1)), x = 1, 2, 3... Let N ∼ Binomial(n, 1−e^−λ ) be another random variable that is independent of the Xi ’s. 1) Show that Y = X1 +X2 + ... + XN has a Poisson distribution with mean nλ.
A charity receives 2025 contributions. Contributions are assumed to be independent and identically distributed with mean...
A charity receives 2025 contributions. Contributions are assumed to be independent and identically distributed with mean 3125 and standard deviation 250. Calculate the probability that the total amount of contributions is greater than $6,320,000.   1. What do I know?   2. What do I want to find out? 3. What do we expect the answer to be? 4. How do I go from what I know to what I want to find? 5. Is the answer consistent with what I expected?  
A: Suppose two random variables X and Y are independent and identically distributed as standard normal....
A: Suppose two random variables X and Y are independent and identically distributed as standard normal. Specify the joint probability density function f(x, y) of X and Y. Next, suppose two random variables X and Y are independent and identically distributed as Bernoulli with parameter 1 2 . Specify the joint probability mass function f(x, y) of X and Y. B: Consider a time series realization X = [10, 15, 23, 20, 19] with a length of five-periods. Compute the...
Let Xi's be independent and identically distributed Poisson random variables for 1 ≤ i ≤ n....
Let Xi's be independent and identically distributed Poisson random variables for 1 ≤ i ≤ n. Derive the distribution for the summation of Xi from 1 to n. (Without using MGF)
Let ?1,?2,…,??be independent, identically distributed random variables with p.d.f. ?(?) = ??^?−1,0 ≤ ? ≤ 1...
Let ?1,?2,…,??be independent, identically distributed random variables with p.d.f. ?(?) = ??^?−1,0 ≤ ? ≤ 1 . c. Show that the maximum likelihood estimator for ? is biased, and find a function of the mle that is unbiased. (Hint: Show that the random variable −ln (??) is exponential, the sum of exponentials is Gamma, and the mean of 1/X for a gamma with parameters ? and ? is 1 / (?(? − 1)). d. Is the estimator you found in...
Suppose that X1, X2, X3, X4 is a simple random (independent and identically distributed) sample of...
Suppose that X1, X2, X3, X4 is a simple random (independent and identically distributed) sample of size 4 from a normal distribution with an unknown mean μ but a known variance 9. Suppose further that Y1, Y2, Y3, Y4, Y5 is another simple random sample (independent from X1, X2, X3, X4 from a normal distribution with the same mean   μand variance 16. We estimate μ with U = (bar{X}+bar{Y})/2. where bar{X} = (X1 + X2 + X3 + X4)/4 bar{Y}...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT