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The random variable \( X \) in this problem is described within the context of a binomial experiment where each integrated circuit either is defective or not, with a probability of being defective given as 0.01. The total number of trials (integrated circuits) is 51, and each trial (the outcome of each circuit being defective or not) is independent.

Here are the choices provided for the definition of \( X \):

1. \( X \) is \(\binom{51}{2}\) defective integrated circuits.
2. \( X \) is a Poisson random variable with \(\lambda = 51\).
3. \( X \) is the probability that there are two defective integrated circuits out of 51 circuits.
4. \( X \) is the number of defective integrated circuits out of 51 integrated circuits.
5. \( X \) is the probability of a Bernoulli trial with \( p = 0.01 \).

The most accurate definition of \( X \) in this scenario is that \( X \) is the number of defective integrated circuits out of 51 integrated circuits. This matches the scenario described where \( X \) counts the number of defective circuits among a fixed number of circuits, each with an independent probability of defectiveness.

Would you like to know more about how this fits within the concepts of probability distributions? If you have any questions, feel free to ask. Here are some related topics you might find interesting:

1. How would the calculation differ if the probability of a circuit being defective was different?
2. What assumptions are made about independence in this scenario?
3. How can you calculate the expected number of defective circuits in this setting?
4. What happens to the distribution of \( X \) as the number of circuits increases?
5. How can the Poisson distribution be used as an approximation in similar problems?

**Tip:** When solving problems involving probabilities and a large number of trials, always verify whether the trials are independent and identically distributed as these assumptions significantly impact the applicability of the binomial and Poisson distributions.

An electronic product contains 51 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. Suppose you want to determine the probability that the number of defective circuits in this product is equal to 2. The best definition of the random variable X, in words, is: (select the best answer).

Explore a binomial probability problem where 51 integrated circuits each have a 0.01 probability of being defective. Learn how to define the random variable X and understand how binomial distribution applies to independent trials.

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