Question: Suppose that an alarm system produces false alarms randomly. The probability that there will be at least one false alarm in a 60 minute period is .001. Let X denote the number of one hour periods in a day in which there are false alarms. Describe the probability distribution of X.
Probability is .001 for one hour and the probability stays the same for each hour right? Since there are 24 hours, wouldn't it just be $.001 * 24 = 0.024$?
The distribution of the number of hours $X$ when the alarm sounds at least once in that hour is Binomial with parameters $n=24$ presumably and $p=0.001$
If instead you are interested in $Y$ the number of times the alarm sounds in a given day then it is a Poisson distribution with parameter $24\lambda$ where $\lambda$ is given by$$1-e^{-\lambda}=0.001$$