## Question

# 5. The geometric and exponential distributions share the lack of memory property, defined as follows: P(X> x+yX >x) = P(X > y). (a) Let

## 5. The geometric and exponential distributions share the lack of memory property, defined as follows: P(X> x+yX >x) = P(X > y). (a) Let X be geometric, with probability function f(x) = p(1 - p) for x = 0,1,2,... and parameter 0 < p < 1. It counts the number of failures before the first success in a sequence of independent Bernoulli trials. Show that the lack of memory property holds, and interpret this result. (b) Let X have an exponential distribution with pdf f(x) = Xe for x > 0 and rate parameter x > 0. Show that the lack of memory property holds. Interpret this result. Hint: Recall that P(A/B) = P(An B)/P(B).

## Step by Step Solution

3.42 Rating (152 Votes )

There are 3 Steps involved in it

### Step: 1

sa Cuien fx P1p As ...### Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

### Step: 2

### Step: 3

## Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started## Recommended Textbook for

### Probability And Statistics

**Authors:** Morris H. DeGroot, Mark J. Schervish

4th Edition

9579701075, 321500466, 978-0176861117, 176861114, 978-0134995472, 978-0321500465

#### Students also viewed these Mathematics questions

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

### Question

Answered: 1 week ago

View Answer in SolutionInn App