Begin2.DVI

Table 11.7 Critical Values tα,n for the Student’s t Distribution with n Degrees of Freedom ∫∞ tα,n √^1 nπ Γ ( n+ 1 2 ) Γ (n 2 ) ...

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Exercises
11-1. A box contains 10 white balls, 3 black balls and 2 red balls. (a) What is the probability of drawing a white ba ...

11-7. Find the arithmetic mean, geometric mean and harmonic mean of the given numbers. (a) 1, 2 , 3 , 4 , 5 , 6 , 7 (b) 1 , 3 , ...

11-11. (Binomial Distribution) The discrete binomial distribution is given by f(x) = {(n x ) px(1 −p)n−x, x = 0, 1 , 2 , 3 ,... ...

11-13. For the given probability density functions f(x), find the cumulative distri- bution function F(x) = ∫x −∞ f(x)dx and th ...

11-18. (Computer Problem for Normal Distribution) There are numerous web sites which use numerical methods to calculate the are ...

11-23. Assume that a given State has regulations specifying that the fluoride lev- els in water may not exceed 1.5 milligrams p ...

11-25. (Binomial distribution) Forty identical transistors are placed on life tests simultaneously and are op- erated for T hou ...

11-27. (Poisson distribution) Let Xdenote a random variable representing the number of light bulbs which fail during a specifie ...

11-30. If Φ(z) = √^1 2 π ∫z −∞ e−ξ (^2) / 2 dξ, find the value of and illustrate with sketches the representations of the follo ...

Chapter 12 Introduction to more Advanced Material The following is a potpourri of selected topics involving mathematical applica ...

We know that the functions f(x)and f−^1 (x)are symmetric about the line y=x as illustrated in the figure 12-1. Examine the figur ...

Example 12-1. (Sum of series) Find the sum of the infinite series 1 1 −^1 4 +^1 7 −^1 10 +^1 13 −^1 16 +··· (12.7) which is an e ...

Example 12-2. (Sum of series) Show that 1 2 · 5 +^1 8 · 11 +^1 14 · 17 +^1 20 · 23 +··· =^1 9 (π 3 + ln2) Solution Let Sdenote t ...

Consider the prism illustrated in the figure 12-2. The angle Aof a prism is known as the apex angle or refracting angle. The ang ...