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JFB-470 5. (a) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(b) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(c) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(d) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(e) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(f) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(g) We shall first find E[N]. We have E[N流入) = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ². and into others (a) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(h) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > based) = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(i) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(j) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(k) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(l) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] ;(1** We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(m) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(n) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(o) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus, the variance of N is given by Var[N] = E[N²] - (E[N])² = 1 / λ².
(p) We shall first find E[N]. We have E[N] = ∫[0,∞] P[N > x] dx. Using integration, we obtain E[N] = 1 / λ. We shall next find E[N²]. We have E[N²] = ∫[0,∞] P[N² > x] dx. Using integration, we obtain E[N²] = 2 / λ². Thus,
28 Mar 2025
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