0.01 Dollars in Rupees
The keyword 0.01 dollars in rupees can be handled as a simple linear conversion, and it also illustrates a standard statistics fact: when a random variable is multiplied by a constant, its mean (expected value) is multiplied by the same constant.
Assumptions used for a complete, well-defined calculation: rupees = Indian rupees (INR) and 1 USD = 83.00 INR.
Step 1: Convert 0.01 dollars to rupees by unit factors
The exchange rate provides a conversion factor:
\[ 1\ \text{USD} = 83.00\ \text{INR} \quad\Longrightarrow\quad 83.00\ \frac{\text{INR}}{\text{USD}} \]
Multiply \(0.01\ \text{USD}\) by the factor so that USD cancels:
\[ 0.01\ \text{USD} \times 83.00\ \frac{\text{INR}}{\text{USD}} = 0.83\ \text{INR} \]
Step 2: Connect the conversion to expected value (mean) in statistics
Suppose \(X\) is a payoff measured in USD (possibly random). Converting to rupees defines a new variable \[ Y = 83.00 \times X \] (measured in INR). Linearity of expectation gives \[ E[Y] = E[83.00 \times X] = 83.00 \times E[X] \]
Therefore, if the expected value is \(E[X] = 0.01\) dollars, then \[ E[Y] = 83.00 \times 0.01 = 0.83\ \text{INR} \]
Compact summary table
| Quantity | Expression | Value |
|---|---|---|
| Exchange rate | \(1\ \text{USD} = 83.00\ \text{INR}\) | \(83.00\ \text{INR per USD}\) |
| Direct conversion | \(0.01\ \text{USD} \times 83.00\ \text{INR per USD}\) | \(0.83\ \text{INR}\) |
| Mean scaling | \(Y = 83.00 \times X \Rightarrow E[Y] = 83.00 \times E[X]\) | \(E[X]=0.01\ \text{USD} \Rightarrow E[Y]=0.83\ \text{INR}\) |