Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. the waiting times x and y (in minutes) of two clie

The waiting times X and Y (in minutes) of two clients A and B who are...

80.2K

Verified Solution

Question

Basic Math

The waiting times X and Y (in minutes) of two clients A and Bwho are standing in line at two different check outs in thesupermarket are modeled as independent, exponential randomvariables with parameter 1.

(a) Find the cumulative distribution function of the randomvariable M :=min{X,Y} where min{x,y} is just the smaller value ofthe two numbers.

(b) Find the probability density function of M. Do you recognizethe socalled probability law or probability distribution of therandom variable M?

(c) What is the probability that both clients wait more than 2minutes?

Answer & Explanation Solved by verified expert
3.8 Ratings (713 Votes)
aFirst we need to find out the distributon of minimum of twoLetSince X and Y are exponentially    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

5. For the function ?(?)=−3?^4 −12?^3 Find the domain and intercepts. Find the critical numbers, intervals where f...

Basic Math
Q

Lynn transfers property (basis of $225,000 and fair market value of $300,000) to Condor Corporation in...

Finance
Q

Matlab code for Gauss Siedel with solved example in Matlab

Advance Math
Q

Show that if 100 people of different heights stand in a line, it is possible that...

Advance Math
Q

Which of the following is true about phylogenetic trees trees should always have at least...

Biology
Q

X is normally distributed random variable with mean 63 and standard deviation 6 The probability...

Geometry
Q

Find the exact value of tan (11?/4) using the unit circle.zero1-12

Basic Math
Q

A rental car company charges 35 plus 35 cents per each mile driven Part1 Which...

Algebra
Q

A company's inventory records Indicate the following data for the month of January: ...

Accounting
Q

Required information Problem 9-31 Production and Direct-Labor Budgets, Activity-Based Overhead Budget (LO 9-3, 9-4, 9-5,...

Accounting
Q

Required information [The following information applies to the questions displayed below.] Tracy...

Accounting
Q

CASE STUDY: 3 Paramount Products SAOG wants to raise OMR 100 Million for diversification project....

Accounting