Let A = (7, 9) ∪ (11, 13) = {x ∈ R : 7 < x < 9 or 11 < x < 13}. Let X ∼ Unif(A). Calculate E[X].
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3. Let X ~ Unif(1,2) be a uniform random variable on the interval (1,2). (a) What is the exact value of the mean of X? (b) Compute or estimate the standard deviation of X. (c) Estimate the expected value E[1/X] accurately to two decimal places.
11 D X where X ~ unif{1, . . . ,0), θ e N. max(X1,-..,An) 2. Suppose that X1,... ,Xn Let T = X(n) =
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Let X have a uniform distribution on the interval (0,1) a. Find the probability distribution of Y-1 Enter a formula in the first box and a number in the second and third boxes corresponding to the range of y. Use * for multiplication, / for divison, for power and in for natural logarithm. For example, (3"у"e 5"y+2)+11*1n(y))/(4xy+3) 4 means (3y-e5 +2 + 11-in y)/(4y+3)4, Use e for the constant e g. e...
A crate with a mass of 189.5 kg is suspended from the end of a
uniform boom with a mass of 95.1 kg. The upper end of the boom is
supported by a cable attached to the wall and the lower end by a
pivot (marked X) on the same wall. Calculate the tension in the
cable.
You'll need to get the various positions from the graph. Many
are exactly on one of the tic marks.)
12 11 10 7...
A crate with a mass of 181.5 kg is suspended from the end of a uniform boom with a mass of 67.3 kg. The upper end of the boom is supported by a cable attached to the wall and the lower end by a pivot (marked X) on the same wall. Calculate the tension in the cable. 12 11 a 10 9 8 7 6 Vertical position, y, 5 4 3 2 1 0 1 2 3 4 5 6...
Four distributions, labeled (a), (b), (c), and (d), are represented below by their histograms. Each distribution is made of 9 measurements. Without performing any calculations, order their respective means Her My Hc, and do (a) (b) 1 2 3 4 5 6 7 R 9 10 11 12 13 14 7 8 9 10 11 12 13 14 (C) (d) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3 4 5 6 7 8...
3. Again, let XXn be iid observations from the Uniform(0,0) distribution. (a) Find the joint pdf of Xo) and X(a) (b) Define R-X(n) - Xu) as the sample range. Find the pdf of R (c) It turns out, if Xi, X, n(iid) Uniform(0,e), E(R)- What happens to E(R) as n increases? Briefly explain in words why this makes sense intuitively.
(c) (20 pts.) Let X have a uniform distribution U(0, 2) and let the considiton; distribution of Y given X = x be U(0, x3) i. Determine f (x, y). Make sure to describe the support of f. ii. Calculate fy (y) iii. Find E(Y).
(20 pts) Let U be a random variable following a uniform distribution on the interval [0 Let X=2U + 1 (a) Is X a random variable? Why or why not? (b) Calculate E[X] analytically
(5 pts) Let U be a random variable following a uniform distribution on the interval [0,1 Let Calculate analytically the variance of X. (HINT: E g(x)f(x)dx, and the p.d.f. 10SzSI 0 o.t.w. f(x) of a uniform distribution is f(x) =