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 ( $\underline{\mathrm{c}}$ ) contradict this claim? Why?

          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 ( $\underline{\mathrm{c}}$ ) contradict this claim? Why?

Added by Daisy J.

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