Amachine relies on the functioning of 3 parts, each of which functions correctly with probability p and does not function with probability (1-p). all three parts function independently of the others, and the machine only works if at least 2 of the 3 parts are operating.
a. compute the probability that the machine is functioning
b. suppose that the value of the probability becomes random. assume that p is a uniform random variable taking real values between 0 and 1, independent of the state of the system, and that all three parts share the same random variable p.
what is the probability that the machine is functioning in this random environment?

the answer for this is 0.25 km. : )

continuous functions:

a function is said to be continuous , if it is an increasing function or decreasing function or both increasing and decreasing function.

if function is increasing continuous function

then for,

if function is decreasing continuous function

then for,

so , in the situation described,for which functions will the y-values be the greatest for every large values of x describes continuous increasing function.as i have defined continuous increasing function

the function having larger slope, will have larger y values , for larger values of   x .

slope between two points (a,b) and (p,q) is given by :

m=

slope in option 1 =75

slope in option 2 =5

slope in option 3 = 200

as the fourth option is a geometric progression, common ratio being 3. as x value increases by 1 , y value increases 3 times.the function can be written as: y=7. [n=0,1,2,3]

option (3) and option (4) is right choice.in each case y value increases with increase in value of x.