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The amount of time that a watch will run without having to be reset is a random variable having an exponential distribution with $\theta=120$ days.

Find the probability that

x is the amount of time a watch will run without being reset.

a. have to be reset in less than 24 hours

I did y is time till watch is reset. $P(Y<24)=P(X \ge 24)$ I did

$\int_{24}^{\infty}\frac{1}{120}e^{(-x/120)}dx$

and got .818 but would this be correct.

Fernando Martinez
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1 Answers1

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Note that $24$ hours is $1$ day. We want $\Pr(X\lt 1)$, or equivalently $\Pr(X\le 1)$, so we want $$\int_0^1 \frac{1}{120}e^{-x/120}\,dx.$$

Remark: An answer of $0.818$ is not physically reasonable. A watch that works nicely on average for $120$ days should not have probability $0.818$ of giving trouble in $24$ hours or less.

André Nicolas
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