When you go fishing, you attach m hooks to your line. Eachtime you cast your lin

Question

When you go fishing, you attach m hooks to your line. Eachtime you cast your line, each hook will be swallowed by a fish with probabiity h,independent of whether any other hook is swallowed. What is the PMF of K, the numberof fish that are hooked on a single cast of the line? When you go fishing, you attach m hooks to your line. Eachtime you cast your line, each hook will be swallowed by a fish with probabiity h,independent of whether any other hook is swallowed. What is the PMF of K, the numberof fish that are hooked on a single cast of the line?

Explanation / Answer

since m hooks are attached and each has a probability h ofbeing swallowed.
fx(k) = Pr(x=k) = # of ways we can select k hooks out of m *Probability that k hooks are hooked * probability that rest m-k arenot hooked ..
In other words this is a binomial distribution with n = m andp = h
PMR fx(k) =mck hk (1-h)(m-k) .
Hope this is helpful. Feel free to ask for anyclarifications.

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