# Question

Show that the normal distribution has

(a) A relative maximum at x = µ;

(b) Inflection points at x = µ – σ and x = µ + σ.

(a) A relative maximum at x = µ;

(b) Inflection points at x = µ – σ and x = µ + σ.

## Answer to relevant Questions

Show that the normal distribution has (a) A relative maximum at x = µ; (b) Inflection points at x = µ – σ and x = µ + σ. Use the Maclaurin’s series expansion of the moment-generating function of the standard normal distribution to show that (a) µr = 0 when r is odd; (b) µr = r! 2r / 2r/2(r/2)! when r is even. If the exponent of e of a bivariate normal density is –1/54 (x2 + 4y2 + 2xy+ 2x+ 8y+ 4) Find σ1, σ2, and ρ, given that µ1 = 0 and µ2 = –1. If a company employs n salespersons, its gross sales in thousands of dollars may be regarded as a random variable having a gamma distribution with α = 80√n and β = 2. If the sales cost is $ 8,000 per salesperson, how ...If Z is a random variable having the standard normal distribution, find (a) P(Z < 1.33); (b) P(Z ≥ – 0.79); (c) P(0.55 < Z < 1.22); (d) P(–1.90 ≤ Z ≤ 0.44).Post your question

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