Following the question above, what is the conditional expectation of
𝑋
1
given
𝑋
2
=
1
?

Question

Following the question above, what is the conditional expectation of 
𝑋
1
 given 
𝑋
2
=
1
?

BlackTom AI · Accepted Answer

To tackle this problem, we first need the joint distribution or additional context from the previous question that defines X1 and X2 and their relationship. Without that information, the conditional expectation E[X1 | X2 = 1] cannot be uniquely determined.

Option 1: None of these answers are correct.
- This statement would be the appropriate choice if, given the missing context, none of the numeric values provided can be justified as E[X1 | X2 = 1]. Since we do not have enough information to compute the conditional expectation, we cannot verify any of the numeric options, so claiming that none of the listed numbers are correct is a plausible stance.

Option 2: -0.596
- This implies a specific computed value for E[X1 | X2 = 1]. To arrive at such a number, we would need the joint distribution or at least the conditional distribution of X1 given X2 = 1. In the absence of that, this value is not justifiable and could be incorrect due to dependence structure, scaling, or rounding that comes from the underlying model.

Option 3: 0.403
- Similar to Option 2, this would require explicit calculation from the joint/dconditional distribution. Without those details, presenting a concrete positive value hinges on assumptions we have no basis for, making this option unreliable in isolation.

Option 4: 1.403
- This is another specific numeric claim for E[X1 | X2 = 1]. Obtaining such a value would demand precise information about the relationship between X1 and X2. In many standard setups, conditional expectations often lie within the range implied by X1's support and the conditioning event, but again, without data, we cannot justify this number. Hence this option is also unsupported given the missing context.

General reasoning across options:
- The conditional expectation E[X1 | X2 = 1] depends on how X1 behaves when X2 is fixed at 1. It cannot be determined from marginal information about X1 alone or from isolated numeric guesses. Any correct choice must be derived from the joint distribution or a derivation provided in the prior part of the question.
- When the necessary information is missing, the most accurate stance is that we cannot confirm a numeric value; therefore, selecting any specific numeric option would be speculative.

In summary, because the problem statement here lacks the essential joint distribution or prior steps needed to compute E[X1 | X2 = 1], none of the numeric options can be verified as correct, and stating that fact is consistent with the requirement to rely on the available data. Thus, without additional context, the claim that none of the listed numbers are correct appropriately reflects the insufficiency of information.

25S-STATS-102B-LEC-3 Quiz 5- Requires Respondus LockDown Browser

Following the question above, what is the conditional expectation of 𝑋 1 given 𝑋 2 = 1 ?

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