Let p=0.23 and q=0.74. What is E(Y)?

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BlackTom AI · Accepted Answer

The question provides p = 0.23 and q = 0.74 and asks for E(Y), but it does not define what Y is or how p and q relate to Y. Without a definition of the random variable Y (its distribution, parameters, and how p and q are involved), the expected value cannot be computed.

To analyze what might be intended, consider common contexts where p and q appear:
- If Y is the number of successes in a single Bernoulli trial, there is no E(Y) because a Bernoulli trial yields either 0 or 1; its expectation would be p, which would be 0.23, not a value like 2.402, and q would be 1 − p = 0.77, not 0.74.
- If Y is the number of successes in n independent Bernoulli trials (a Binomial(n, p) variable), then E(Y) = n p. With p = 0.23, to obtain E(Y) = 2.402 you would need n = E(Y)/p ≈ 2.402 / 0.23 ≈ 10.43, which is not an integer and thus does not correspond to a standard binomial with a whole number number of trials. This mismatch suggests either n is not an integer (not a valid binomial parameter) or the given numbers do not align with a binomial model.
- If Y is geometrically distributed with success probability p, then E(Y) = 1/p = 1/0.23 ≈ 4.347, which again does not match 2.402, and q would be 1 − p = 0.77, not 0.74.
- If Y is some linear function of p and q, or if p and q represent other quantities (like probabilities of two complementary events that are not constrained to sum to 1), we still need the exact relationship to Y to compute E(Y).

Notice also that q is given as 0.74. In many probability problems, q denotes 1 − p, which would be 0.77 here if p = 0.23. The fact that q ≠ 1 − p indicates either:
- a nonstandard notation is being used, or
- there is a missing piece of information about how p and q relate to Y, or
- there is a possible inconsistency in the provided values.

Because the problem statement lacks the definition of Y and how p and q interact with Y, any calculation of E(Y) would be speculative. To proceed correctly, one would need:
- The distribution of Y (e.g., Bernoulli, Binomial, Geometric, etc.).
- The exact formula for E(Y) in terms of the given parameters, or at least the relationship between Y and p, q (e.g., Y ~ Binomial(n, p) with n known, or Y defined as a function of p and q).
- Clarification on what q represents in this context (is q = 1 − p, or is q an independent parameter with its own meaning?).

If you can provide the definition of Y or the intended model (e.g., Y ~ Binomial(n, p) with a specified n, or a formula like E(Y) = f(p, q)), I can compute the exact value of E(Y) and explain the steps. As it stands, the information given is insufficient to determine E(Y) reliably.

COMM_V 190 101-104 2025W1 2025W1 COMM 190 Final Exam - TUE Dec 09 2025 - Requires Respondus LockDown Browser

Let p=0.23 and q=0.74. What is E(Y)?

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