# Probability

Suppose that you have two laptops, both of which you begin using at time 0. Each laptop will eventually fail, and we model each one's lifetime as exponentially distributed with the same parameter λ. The lifetimes of the two laptops are independent. One of the laptops will fail first, followed by the other. Define T1 as the time of the first failure and T2 as the time of the second failure.

In parts 1, 2, 4, and 5 below, your answers will be algebraic expressions. Enter 'lambda' for λ and use 'exp()' for exponentials. Follow standard notation.

Determine the PDF of T1.

For t>0,fT1(t)=

Let X=T2−T1. Determine the conditional PDF fX∣T1(x∣t).

For x,t>0,fX∣T1(x∣t)=

Is X independent of T1?

Yes, they are independent - unanswered
Determine the PDF fT2(t).

For t>0,fT2(t)=

E[T2]=

1. 👍 0
2. 👎 0
3. 👁 269
1. 1) 2*lambda*exp(-2*lambda*t)
2) lambda*e^(-lambda*x)
3) yes
4) 2*lambda*exp(-lambda*t)*(1-exp(-lambda*t))
5) 3/(2*lambda)

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Physics

A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. Suppose we repeat the experiment but, instead of starting from rest, the

2. ### Calculus

A shop is open 9 AM - 7 PM. The function r(t), graphed above, gives the rate at which customers arrive (in people/hour) at time t, where t measures time in hours since 9 AM. Suppose that the salespeople can serve customers at a

3. ### physics

You are driving through town at 14 m/s when suddenly a car backs out of a driveway in front of you. You apply the brakes and begin decelerating at 3.3 m/s2.How much time does it take to stop? After braking half the time found in

4. ### English

Which option below would make the following statement parallel? She insisted the presentation not only begin on time but: A. it will be closed to anyone who arrived late. B. conclude 10 minutes earlier than scheduled. C. that she

1. ### Calculus

(Bees collecting pollen and nectar - Optimization) Many bees collect both pollen and nectar. Pollen is used for protein, and nectar is used for energy. Suppose the amount of nectar harvested during t seconds on a flower is:

2. ### Math

The average travel time to work for a person living and working in​ Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately

3. ### pre cal

The vector u = (4300, 5200) gives the number of units of two models of laptops produced by a company. The vector v = 1800, 1200 gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector

4. ### Math

The average travel time to work for a person living and working in​ Kokomo, Indiana is 19 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately

1. ### Math

A quality control specialist for a large computer store conducted a random sample of 150 laptops from its stock. She found 3 did not turn on and 5 required system updates to run properly. What is a reasonable probability model for

2. ### Statistics

The records of a computer retail store show that out of the 100 customers who purchased a desktop computer last month, 69 also purchased a service plan that extends the warranty for an extra year. Out of the 25 customers who

3. ### English

which statement from "Mexicans Begin Jogging" best supports its theme of the diversity that is at the heart of being an American? A."since I was on his time, I ran..." B."Their vans and my boss waved for us to run." C."No time for

4. ### math, probability

Suppose that we have three engines which we turn on at time 0. Each engine will eventually fail, and we model each engine's lifetime as exponentially distributed with parameter lambda. One of the engines will fail first, followed