The family of bell-shaped curvesy 1 s2 ex 22 2occurs in probability and statistics
Chapter 4, Problem 58(choose chapter or problem)
The family of bell-shaped curvesy 1 s2 ex 22 2occurs in probability and statistics, where it is called the normal density function. The constant is called the mean and the positive constant is called the standard deviation. For simplicity, lets scale the function so as to remove the factor and lets analyze the special case where . So we study the functionfx ex22 2(a) Find the asymptote, maximum value, and inection points of . (b) What role does play in the shape of the curve? ; (c) Illustrate by graphing four members of this family on the same screen.
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