Question

Consider a loaded six-sided die that is twice as likely to roll an even number as an odd number. Let X be a random variable for the value that is rolled from the die. What is the probability distribution of X?

1) Uniform distribution
2) Binomial distribution
3) Geometric distribution
4) Poisson distribution

Answer 1

The probability distribution of a loaded die that is twice as likely to roll an even number as an odd number is not uniform, binomial, geometric, or Poisson. It has a distinct distribution based on the biased probabilities of the outcomes.

Step-by-step explanation:

The question revolves around finding the probability distribution of the random variable X, which denotes the outcome when rolling a loaded six-sided die that is biased towards even numbers. Since the die is twice as likely to roll an even number as an odd number, the probability is not the same for all outcomes, and so it does not follow a uniform distribution. As the outcomes are discrete and there is no fixed number of trials, nor success on certain trials as in binomial distribution, and since it neither deals with the number of trials until the first success as in a geometric distribution nor with the occurrence of events in a fixed interval as in a Poisson distribution, none of these mentioned distributions appropriately describe the probability distribution of X. Instead, X has a distinct distribution based on the biased probabilities of rolling each number on the die.