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![6. Suppose that a random variable X has a continuous
distribution for which the p.d.f. f is as follows:
2x for 0 < x < 1,
f(x) = | 2x
0
otherwise.
Determine the value of d that minimizes
(a) E[(X-d)2] and (b) E(|X - dl).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fb406b3-dfb5-4d65-a424-9ec71ae4c6de%2F6d61b322-d8ca-49ac-9874-86a73ad92e62%2Fswil0hk_processed.jpeg&w=3840&q=75)
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- If X and Y are two independent uniform distribution with X(0 ,4) and Y(0,6). Find the joint pdf f (x.y). Find P(2.5<X<3.5,1<Y<4)In the conclusion of the Mean Value Theorem for the function f(x) = x, [0, 1] %3D 29 - Find the value or values of c that satisfy the equation f(b) - f(a) b- a f'(c) %3D O A) 5 O B) 9/33 C) 8/27 O D) 6/33 O E) 5/27Suppose that the p.d.f. of X is as given f(x)=4x-1 for 0≤x≤1 and 0 otherwise Find the pdf of Y=X1/2.
- Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x) = 10 x over the interval [10, 10]. In other words, find c E [10, 10] such that f(c) This function has two values, c₁ and c₂, where c₁ < C₂. 41 = 10 10-11-10) / 10 -10) / f(x)dx. - 10 - C2State the CLT for independent identically distributed real RVs with mean u and variance a². Suppose that X. X,. . . are independent identically distributed random variables each uniformly distributed over the interval [0, 1]. Calculate the mean and variance of In X. Suppose that 0If Y = InX has a N (0, 1) distribution then E (X²) is equal to2. Let dt Find the average %3D value of f on the interval [o, 1A R.V X is uniformly distributed over(-1,1) and Y=X². Check if X and Y are correlated?Suppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤ T8. Assume that X is a continuous random variable with pdf 1 if -6Ук. Suppose that Y₁. Y₂; Yn 15. 2 from Function random Sample a population with probability density f(y) = find the maximum BY 1-B B like hood ozy 21: B >0 Elsewhere Estimator of BGiven that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: The marginal function of X ,f1(X)Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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