Q.6.27 Establish Equation (6.2)聽by dif... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 6: Q.6.27 (page 277)

Establish Equation $(6.2)$ by differentiating Equation $(6.4)$ .

Short Answer

Expert verified

On differentiating equation $(6.4)$ we get equation $(6.2)$ .

Step by step solution

Differentiation

Differentiation is a technique for calculating a derivative, which is the rate of change of a function's output $y$ in relation to the change of a variable $x$ .

Explanation :

$F_{x_{i j}} (y) = {鈭�}_{k = j}^{n} (\begin{matrix} n \\ k \end{matrix}) {[F (y)]}^{k} {[1 - F (y)]}^{n - k} . . . . . . . . . . (6.4)$

Differentiating both sides with respect to y, then

$f_{X_{j}} (y) = {鈭�}_{k = j}^{n} (\begin{array}{l} n \\ k \end{array}) k F {(y)}^{k - 1} f (y) [1 - F (y)]^{n - k} - {鈭�}_{k = j}^{n} (\begin{array}{l} n \\ k \end{array}) F {(y)}^{k - 1} (n - k) [1 - F (y)]^{n - k - 1} f (y) = {鈭�}_{i = j}^{n} \frac{n!}{(n - k)! (k - 1)!} F {(y)}^{k - 1} f (y) [1 - F (y)]^{n - k} - {鈭�}_{k = j + 1}^{n} \frac{n!}{(n - k)! (k - 1)!} F^{k - 1} (y) f (y) [1 - F (y)]^{n - k} byj = k + 1 = \frac{n!}{(n - j)! (j - 1)!} F^{j - 1} (y) f (y) [1 - F (y)]^{n - j}$

which is the same as the equation $(6.2)$

Hence proved.

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91影视

Establish Equation $(6.2)$ by differentiating Equation $(6.4)$ .

Short Answer

Step by step solution

Differentiation

Explanation :

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91影视

Establish Equation (6.2)by differentiating Equation6.4.

Short Answer

Step by step solution

Differentiation

Explanation :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Calculus

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Establish Equation $(6.2)$ by differentiating Equation $(6.4)$ .