Let the distribution of X be N(μ, σ2). Show that the points of inflection of the graph of the pdf of X occur at x = μ ± σ.
Answer to relevant QuestionsThe weekly gravel demand X (in tons) follows the Pdf However, the owner of the gravel pit can produce at most only 4 tons of gravel per week. Compute the expected value of the tons sold per week by the owner. Suppose that the length W of a man’s life does follow the Gompertz distribution with λ(w) = a(1.1)w = ae(ln 1.1)w, P(63 < W < 64) = 0.01. Determine the constant a and P(W ≤ 71 | 70 < W). The torque required to remove bolts in a steel plate is rated as very high, high, average, and low, and these occur about 30%, 40%, 20%, and 10% of the time, respectively. Suppose n = 25 bolts are rated; what is the ...Let the joint pmf f(x, y) of X and Y be given by the following: (x, y) f(x, y) (1, 1) ....... 3/8 (2, 1) ....... 1/8 (1, 2) ....... 1/8 (2, 2) ....... 3/8 Find the two conditional probability mass functions and the ...Let X and Y have the joint pdf f(x, y) = x + y, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. (a) Find the marginal pdfs fX(x) and fY(y) and show that f(x, y) ≠ fX(x)fY(y). Thus, X and Y are dependent. (b) Compute (i) μX, (ii) μY, ...
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