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- 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is P(X = 2)? What is the P(X = −1)? (To do this problem think about the definition of MX(t) as E(etX) = Σ ext P(X = x)).If T is nilpotent of index k. Show that Tn , n>1 is nilpotent of index k.1. Find the natural cubic spline sN (x) passing through the 3 points (xj, yj) given by (0, 2), (2, 3), and (3, 1).Then evaluate sN (1).
- We now need to attempt to find an exact value for n such that P(r ≥ 1) = 0.99. Clearly, if the bank has any chance of detecting a burglar they will need to have at least one alarm installed. So, we know that, minimally, n must be at least 1.Since n must be at least 1, suppose we start by trying n = 2, where there will be two alarms. When there are two alarms, r ≥ 1 means either one or both alarms could detect the burglar. If neither alarm detects the burglar it is considered a failure. Therefore, P(r ≥ 1) can be calculated using either of the following formulas. P(r ≥ 1) = P(1) + P(2) P(r ≥ 1) = 1 − P ( ___ ) fill in the blankAnswers: 1. Fobt = 7.54, reject H0;, do Wilcoxon; Tobt = 90.5, reject H0 2. Fobt = 10.08, reject H0, do Wilcoxon; Zobt = 1.197, do not reject H0 3. t = .163, Do not reject H0; no evidence that the device increases cars' mpg6. If u=u(y-x/xy,z-x/xz) prove tha x^delu/delx+y^delu/dely+z^delu/delz=0
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