Compute wallet-link probabilities and expectation

Q: Compute wallet-link probabilities and expectation

This question evaluates understanding of basic probability concepts including Bernoulli trials, expectation, independence assumptions, and the use of Poisson approximations for rare-event modeling.

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Question

Wallet Linking: Expectation and Probability (with Poisson Approximation)

You have n users. Each user links a wallet with probability p, independently of other users. Let X be the number of users who link a wallet.

What is the expected number of users who link a wallet, E[X]?
What is the probability that at least one user links a wallet, P(X ≥ 1)?
- State clearly any independence assumptions you use.
- When p is small and n is large (with λ = np), provide a Poisson approximation for P(X ≥ 1) and the first-order error term of this approximation.

Compute wallet-link probabilities and expectation

Wallet Linking: Expectation and Probability (with Poisson Approximation)

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Compute wallet-link probabilities and expectation

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Wallet Linking: Expectation and Probability (with Poisson Approximation)

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