Consider a system consisting of three components as pictured. the system will continue to function as long as the first component functions and cither component 2 or component 3 functions. let x1, x2, and x3 denote the lifetimes of components 1, 2, and 3, respectively. suppose the x, s are independent of one another and each x1 has an exponential distribution with parameter. let y denote the system lifetime. obtain the cumulative distribution function of y and differentiate to obtain the pdf. [hint: f(y) = p(y y): express the event [ y y] in terms of unions and/or intersections of the three events {x1 y}, {x2 y}, and {x3 y}.] compute the expected system lifetime.

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

conservation of mass

mass before something happens = mass afterwards