Question 5:Definition: Let X be a population random variable and let f, (x;0) be the density function for X. LetO be an estimator for the parameter 0 based on a random sample of observations from X.1) We define the bias of Ô by B(Ô) = E ô–0|= EE[ô]-0.2) If E 0 = 0 then we say 0 is an unbiased estimator of 0, in which case B(0) = 0.Let X be a Bernoulli Trial population with parameter 0 representing the probability of a success. LetX1,...,X, be a random sample from X and let Y = X (1-X) be an estimator for o = 0(1-0).••.A. Find a constant c such that cY is an unbiased estimator for o, = 0(1-0).B. Calculate the bias B(Y)C. Interpret this bias in the context of the problem.

Answered: Image /qna-images/answer/db456e74-7ffb-441a-9147-75474e2cf82c.jpg

Answered: Let X be a Bernoulli Trial population…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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QUESTION 10 Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2. What are the values for a and b? a. 2 and 6 b. Cannot answer with the information given. c. 0 and 4 d. Can be any range of x values whose length (b − a) equals 4. QUESTION 11 The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a ≤ x ≤ b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices. QUESTION 12 Which of the following is true about f(x) when X has a uniform distribution over the interval [a, b]? a. The values of f(x) are different for various values of the random variable X. b. f(x) equals one for each possible value of X. c. f(x) equals one divided by the length of the interval from a to b.…
Question 1 : Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is f(x) = 3 x 2 (400)3 , 0 ≤ x < 400. (a) Compute the probability the a certain part will fail in less than 200 weeks. (b) Compute the mean lifetime of a part and the standard deviation of the lifetime of a part. (c) To decrease the probability in part (a), four independent parts are placed in parallel. So all must fail, if the system fails. Let Y = max{X1, X2, X3, X4} denote the lifetime of such a system, where Xi denotes the lifetime of the ith component. Show that fY (y) = 12 y 11 (400)12 , y > 0. Hint : First construct FY (y) = P(Y ≤ y), by noticing that {Y ≤ y} = {X1 ≤ y} ∩ {X2 ≤ y} ∩ {X3 ≤ y} ∩ {X4 ≤ y}. (d) Determine P(Y ≤ 200) and compare it to the answer in part (a)
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Theorem A at Section 8.8.1 saysA necessary and sufficient condition for T(X1,..., Xn) to be sufficient for a parameter θ is that the joint probability function (density function or frequency function) factors in the formf(x1,...,xn|θ) = g[T(x1,...,xn),θ]h(x1,...,xn)
QUESTION 2 Delta Airlines quotes a flight time of 4 hours, 3 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 4 hours and 4 hours, 12 minutes. (a) Show the graph of the probability density function for flight time. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 234, 240, 246, 252. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/12, 1/6, 1/4. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/12 unit long vertical line segment begins at 240 on the horizontal axis. A 1/12 unit long vertical line segment begins at 252 on the horizontal axis. A 12 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/12 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded…
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