Let A, B, C1,.. , Cn be events on a probability space (0, P). Suppose that...

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For n N, let cn be defined by cn := 1/1 + 1/2 + +1/n - ln n. Show that (cn) is a decreasing sequence of positive numbers. Show that if we put then the sequence (bn) converges to ln 2. [bn = c2n - cn...
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Let A, B be events taken from a sample space (with Pr(A) > 0 and Pr(B) > 0). If Pr(B|A)
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Verify that \(\left|\Delta v_{\mathrm{u} x} ight| /\left|\Delta v_{\mathrm{s} x} ight| \approx 1 / 3\) for the two carts in Figure 4.9. Figure 4.9 Velocity-versus-time graph for a standard cart and a...
What is the ratio of the \(x\) components of the change in velocity for the plastic and metal carts, \(\Delta v_{\mathrm{p} x} / \Delta v_{\mathrm{m} x}\), in Figure 4.10? Figure 4.10...
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