Suppose three marksmen shoot at a target. The ith marksman fires ni times, hitting the target each time with probability Pi, independently of his other shots and the shots of the other marksmen. Let X be the total number of times the target is hit. Is this distribution binomial?

Distribution is NOT binomial.

Step-by-step explanation:

In order to be a binomial distribution, the probability of success for each individual trial must be the same. Since each marksman hits the target with probability Pi, the probability of success (hitting the target) is not necessarily equal for all trials. Therefore, the distribution is not binomial.

In this case, the distribution would only be binomial if Pi was the same for every "ith" marksman.