Consider a segment of an electrical circuit with three relays connected in parallel. Current flows through the circuit if at least one relay is functioning when the "system" is turned on. Suppose the relays function independently and assume their lifetimes are distributed exponentially with a mean of 30 days. (a) What is the probability a relay lasts longer than 60 days? (b) What is the probability that the “system" will last longer that 60 days.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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This is a Statistics problem. Please explain each step thoroughly and code in R, if needed. 

**Problem Scenario:**
Consider a segment of an electrical circuit with three relays connected in parallel. Current flows through the circuit if at least one relay is functioning when the "system" is turned on. Suppose the relays function independently and assume their lifetimes are distributed exponentially with a mean of 30 days.

**Questions:**

(a) What is the probability a relay lasts longer than 60 days?

(b) What is the probability that the "system" will last longer than 60 days?
Transcribed Image Text:**Problem Scenario:** Consider a segment of an electrical circuit with three relays connected in parallel. Current flows through the circuit if at least one relay is functioning when the "system" is turned on. Suppose the relays function independently and assume their lifetimes are distributed exponentially with a mean of 30 days. **Questions:** (a) What is the probability a relay lasts longer than 60 days? (b) What is the probability that the "system" will last longer than 60 days?
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