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It's several attempts to start an engine are made. Each attempt takes time $\tau$ and ends with success (starting the engine), independently of the others with probability $p = 0.6$. Find the distribution of the total time $T$ required to include the engine and its average value.

We have discrete random variable $T$. So $E(X)=\sum\limits_{}^{}x_ip_i$. I have no idea...

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1 Answer 1

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Hint:

Let $N$ be the number of trials until success with chance $p = .6$. Since each trial is independent, it follows a geometric distribution on $\{1,2,3,\dotsc\}$. It appears that $\tau$ is fixed, and so the total time until success is $$T = \tau N.$$

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