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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