# Question: Show that the normal distribution has a A relative maximum

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.

**View Solution:**## Answer to relevant Questions

Show that the differential equation of Exercise 6.30 with b = c = 0 and σ > 0 yields a normal distribution. In exercise If we let KX(t) = lnMX – µ(t), the coefficient of tr/r! in the Maclaurin’s series of KX(t) is called the rth cumulant, and it is denoted by kr. Equating coefficients of like powers, show that (a) k2 = µ2; (b) k3 = ...If X and Y have the bivariate normal distribution with µ1 = 2, µ2 = 5, σ1 = 3, σ2 = 6, and ρ = 2/3 , find µY|1 and σY|1. The amount of time that a watch will run without having to be reset is a random variable having an exponential distribution with θ = 120 days. Find the probabilities that such a watch will (a) Have to be reset in less than ...If Z is a random variable having the standard nor–mal distribution, find the probabilities that it will take on a value (a) Greater than 1.14; (b) Greater than –0.36; (c) Between –0.46 and – 0.09; (d) Between ...Post your question