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A box contains five keys, only one of which will open a
Chapter 4, Problem 2E(choose chapter or problem)
A box contains five keys, only one of which will open a lock. Keys are randomly selected and tried, one at a time, until the lock is opened (keys that do not work are discarded before another is tried). Let Y be the number of the trial on which the lock is opened.
a Find the probability function for Y.
b Give the corresponding distribution function.
c What is \(P(Y<3)\)? \(P(Y \leq 3)\)? \(P(Y=3)\)?
d If Y is a continuous random variable, we argued that, for all \(-\infty<a<\infty\), \(P(Y=a)=0\). Do any of your answers in part (c) contradict this claim? Why?
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QUESTION:
A box contains five keys, only one of which will open a lock. Keys are randomly selected and tried, one at a time, until the lock is opened (keys that do not work are discarded before another is tried). Let Y be the number of the trial on which the lock is opened.
a Find the probability function for Y.
b Give the corresponding distribution function.
c What is \(P(Y<3)\)? \(P(Y \leq 3)\)? \(P(Y=3)\)?
d If Y is a continuous random variable, we argued that, for all \(-\infty<a<\infty\), \(P(Y=a)=0\). Do any of your answers in part (c) contradict this claim? Why?
ANSWER:Step 1 of 8
A probability function is a mathematical function that gives the probability of each possible outcome of a random experiment. It is also known as a probability mass function (PMF) for discrete random variables and a probability density function (PDF) for continuous random variables.
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Review this written solution for 31668) viewed: 5089 isbn: 9780495110811 | Mathematical Statistics With Applications - 7 Edition - Chapter 4 - Problem 2e
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