Question: Let x > 0 be a lifetime with survival function s(x). Let x > 0, t > 0 be two times. Suppose that P(X

Let x > 0 be a lifetime with survival function s(x). Let

Let x > 0 be a lifetime with survival function s(x). Let x > 0, t > 0 be two times. Suppose that P(X > x) > 0. Show that: a) P(x a)= S(x)-S(a+t) S(x) b) P(X>x+t] X>a) = S(a+t)

Step by Step Solution

★★★★★

3.49 Rating (149 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Suppose that S is regarded as a function of P and T. Show that TdS= CpdT- aTVdp. Hence, show that the energy transferred as heat when the pressure on an incompressible liquid or solid is increased by...

Let X and P be random variables. Suppose that the conditional distribution of X given P = p is the binomial distribution with parameters n and p. Suppose that the distribution of P is the beta...

Let X Geom(p). Let s 0 be an integer. a. Show that P(X > s) = (1 p)s. b. Let t 0 be an integer. Show that P(X > s + t | X > s) = P(X > t). This is called the lack of memory property. c. A penny...

3. Suppose X is a random variable with survival function s (3 ) = exp (-22 for x 20. (a) Compute Var (X). (b) Compute E (min (X, c)) for all c 2 0. (c) Compute Cov (min (X, X' ) , max (X, X? ) )

(30 points) Fix x 2 0, and define an " Esscher-transformed" frailty random variable As with probability density function (or discrete probability mass function in the discrete case) fAs (A) =...

Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and...

Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.3. Recall that in a random...

Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.7 (p. 38). Recall that in a random sample of 106 social (or...

The bar graph shows the population of the United States, in millions, for six selected years. a. Write a function that models the total U.S. population, P(x), in millions, x years after 1985. b....

Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.7 (p. 38). Recall that in a random sample of 106 social (or...

The purpose of this assessment is to evaluate the financial condition and performance of Southwest Airlines. Research & complete the following financial ratios and show the work. profitability ratio...

6. Permanent tooling is to be evaluated for an operation and product. Let the estimated unit savings in direct labor be $.20 for a part if tooling is used, burden on labor saved -35%, cost of each...

Consider a person you believe served as an excellent role model as a leader. This could be a friend, coach, teacher etc..or anyone else you know. Andrea the following What traits, skills, and...

Presentation Content You have been hired as a business process consultant for a fast food restaurant to strategically reorganize, standardize, and improve their service processes through the use of...

What one modification would you recommend to the "Temporal-Three" evacuation signal to increase its "recognition" and perception of "urgency". In your response justify your modification financially...

A crate starts from rest and is pulled by a force P of 500 N. Determine the speed of the crate after 4 s if between crate and surface is 0.2. Take mass of crate as 80 kg. REMEMBER: use Fdt = m(v -v)...

PROMPT: An officer of Westway Corporation recently commented that when he receives the firm's financial statements, he looks at just the bottom line o the income statement-the line that shows the net...

Southwestern Punch was made by Frutayuda, Inc. and sold in 12-ounce cans to benefit victims of Hurricane Zero. The mean number of ounces placed in a can by an automatic fill pump is 11.7 with a...

Let H be a nonempty, closed, bounded subset of Rn. a) Suppose that f : H Rm is continuous. Prove that is finite and there exists an x0 H such that ||f(x0)|| = ||f||H. b) A sequence of functions fk: H...

Suppose that a a) Prove that if f is continuous at x0 [a, b] and f(x0) 0, then b) Show that if f is continuous on [a, b], then ba |f(x)dx = 0 if and only if f(x) = 0 for all x [a, b]. c) Does part...

Assume that ex is differentiable on R with (ex) = ex. a) Show that the following function is differentiable on R with f(0) = 0: b) Do analogous statements hold for f(n)(x) when n = 2, 3,...? f(x) = x...

2.6. Give an example of a variable that is (a) categorical, (b) quantitative, (c) ordinal scale, (d) nominal scale, (e) discrete, (f) continuous, (g) quantitative and discrete.

1.17. In a recent survey by Eurobarometer ofEuropeans about energy issues and global warming,1 one question asked, "Would you be willing to pay more for energy produced from renewable sources than...

2.3. Which scale of measurement (nominal, ordinal, or interval) is most appropriate for (a) Attitude toward legalization of marijuana (favor, neutral, oppose) (b) Gender (male, female) (c) Number of...