Suppose q=0.27. Find the expected value of X.

Question

BlackTom AI · Accepted Answer

The prompt asks: 'Suppose q=0.27. Find the expected value of X.' However, there are no answer options provided, and key contextual details are missing.

First, I restate what is needed to compute an expected value for common distributions:
- If X ~ Binomial(n, p), then E[X] = n p. Here p is the probability of success, which would be p = 1 − q if q represents the probability of failure. With q = 0.27, p = 0.73, but we still need the number of trials n to determine E[X]. Without n, the product n p cannot be computed.
- If X follows a geometric distribution (number of trials until the first success), and p = 1 − q = 0.73, then E[X] = 1/p ≈ 1.37. This is another possible interpretation, but it hinges on the assumption that X is geometric, which is not stated.
- If X is some other distribution (negative binomial, hypergeometric, normal approximation, etc.), the formula for E[X] would be different, and again we would need additional parameters (such as sample size, population size, or mean of a normal variable) to compute a numeric value.

Because the problem statement provides q but no n or distribution type for X, multiple common interpretations yield different requirements and, in many cases, inconsistent results when attempted with the given q alone. For example, if one were to force E[X] = 1.96 under a binomial interpretation with p = 0.73, one would require n = E[X]/p ≈ 1.96 / 0.73 ≈ 2.685, which is not an integer and therefore not feasible as a binomial trial count. This inconsistency further signals that the necessary information is missing or the provided answer may be based on a specific, unstated context.

In light of these observations, the primary issue is that the question lacks essential details (the distribution of X and the parameter n or other relevant parameters). To proceed unambiguously, one would need:
- The distribution family of X (e.g., binomial, geometric, etc.).
- The corresponding parameters (e.g., n for binomial, p for geometric or for binomial via p = 1 − q).
- Any additional constraints or context that tie q to the distribution parameters.

Until those details are supplied, a definitive numerical value for E[X] cannot be determined from the information given. If you can provide the distribution of X and its parameters, I can compute E[X] step by step and show how the result aligns with the chosen model.

COMM_V 190 101-104 2025W1 Final Exam - Practice Questions - Second Half

Suppose q=0.27. Find the expected value of X.

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