6. A lightbulb will work until failure. Being a cheap Chinese import the lightbulb has a 0.001 chance of failure each time you turn on the lightbulb. We can think of failure when you turn on the lights as a Geometric Distribution D. State the Probability Distribution Function for this Geometric Distribution E. What is the expected number of times you can turn on the lights before this bulb fails? F. Find P(fails after turning on lights 2001 times) to the nearest ten millionths (hint: the next 3 digits are 9's;
6. A lightbulb will work until failure. Being a cheap Chinese import the lightbulb has a 0.001 chance of failure each time you turn on the lightbulb. We can think of failure when you turn on the lights as a Geometric Distribution D. State the Probability Distribution Function for this Geometric Distribution E. What is the expected number of times you can turn on the lights before this bulb fails? F. Find P(fails after turning on lights 2001 times) to the nearest ten millionths (hint: the next 3 digits are 9's;
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:6. A lightbulb will work until failure. Being a cheap Chinese import the lightbulb has a
0.001 chance of failure each time you turn on the lightbulb. We can think of failure
when you turn on the lights as a Geometric Distribution
D. State the Probability Distribution Function for this Geometric Distribution
E. What is the expected number of times you can turn on the lights before this bulb
fails?
F. Find P(fails after turning on lights 2001 times) to the nearest ten millionths (hint:
the next 3 digits are 9's;
Expert Solution
Step 1
(a) Probability distribution function for the given Geometric distribution :
Let p be the probability that light bulbs fails after x number of turning on the light, then the probability distribution function is given by,
P(X=x) = p × (1–p)x–1 ; x ≥ 1
EXPLANATION:
A random variable X is said to follow Geometric distribution if it's probability density function (pdf) is given by,
P(X =x) = p × (1–p)x–1
( where, x ≥ 1 and 0<p≤1)
x = Number of trials,
p = probability of success.
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