Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:

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Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:

(a) lambda=.5

Pr=

(b) lambda=0.9

Pr=

(c) lambda=1.1

Pr=

answer : a) P( X> 5 ) = 0.0821

              b) P( X > 5 ) = 0.0111

              c) P ( X > 5 ) = 0.00409

Step-by-step explanation:

A) P( X > 5 ) = exp ( - λ * x )

   = ≈ 0.082

B)  P( X > 5 ) = exp ( - λ * x )  

  = ≈ 0.0111

C) P( X > 5 ) = exp ( - λ * x )  

 =  ≈ 0.00409

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

maybe showing the graph would

step-by-step explanation:

-387129 iq