Business Context

StreamCart, a subscription video platform, is testing a sign-up promotion where each new subscriber spins a prize wheel. Finance wants to know the expected payout per spin before approving a full launch.

Problem Statement

Each new subscriber gets exactly one spin. The wheel has six possible outcomes with different probabilities and prize values. Calculate the expected prize cost per spin, the variance and standard deviation of payout, and the expected net value after accounting for expected subscriber revenue.

Given Data

The expected gross revenue from a newly acquired subscriber is estimated at $18.50.

Requirements

1. Verify that the outcome probabilities form a valid probability distribution.
2. Compute the expected prize payout per spin.
3. Compute the variance and standard deviation of the payout distribution.
4. Compute the expected net value per acquired subscriber after prize cost.
5. State whether the promotion is profitable on average based on expected value alone.

Assumptions

• Each spin is independent.
• Prize values represent the company’s expected cost, not retail price.
• The $18.50 expected revenue already reflects average retention and payment behavior.
• Ignore operational costs beyond the listed prize costs.