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The provided image contains a problem regarding the calculation of life expectancy from a life table, specifically for a dataset referred to as "GSB 519 Male Survivors" from a file. Here's a breakdown of the key elements and tasks:

### Key Elements of the Problem:
1. **Variables**:
   - \( x \): Age.
   - \( l_x \): Number of people alive at age \( x \) in the Male Survivors life table.
   - \( P_{x+j} \): Probability of surviving \( j \) years after age \( x \), calculated as \( P_{x+j} = \frac{l_{x+j}}{l_x} \).
   - \( LE_x \): Life expectancy at age \( x \).

2. **Life Expectancy Formula**:
   \[
   LE_x = 0.5 + P_{x+1} + P_{x+2} + P_{x+3} + \dots
   \]
   This formula continues until the end of the life table, summing up the probabilities of surviving additional years beyond \( x \).

3. **Expected Age at Death**:
   The expected age at death for a person currently age \( x \) is \( x + LE_x \).

4. **Tasks**:
   - Create an **Excel spreadsheet** that computes life expectancies for ages \( x = 0 \), \( 40 \), and \( 80 \) based on the data from the Male Survivors life table.
   - Corresponding expected ages at death are also required.
   - The Excel sheet should show all calculations and be included in a report.

### Steps for Excel Calculation:
1. **Data Input**: 
   - You will need to extract the values of \( l_x \) from the "Male Survivors" life table for each relevant age group (e.g., \( x = 0 \), \( 40 \), \( 80 \)).
   
2. **Calculate Survival Probabilities**:
   - For each age \( x \), calculate \( P_{x+j} = \frac{l_{x+j}}{l_x} \) for the next several years (until the table ends).
   
3. **Sum Probabilities**:
   - For each age \( x \), sum the survival probabilities for future years (as given in the formula).

4. **Compute Life Expectancy**:
   - Use the formula \( LE_x = 0.5 + P_{x+1} + P_{x+2} + \dots \) to calculate the life expectancy for each of the specified ages \( x \).

5. **Expected Age at Death**:
   - Calculate the expected age at death as \( x + LE_x \) for each \( x \).

Would you like assistance in building the formulas or structuring the Excel sheet?

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### 5 Related Questions:
1. How do you interpret the probability of surviving to the next year in a life table?
2. What factors can affect the life expectancy in different populations?
3. Why is \( 0.5 \) added to the life expectancy formula?
4. How does life expectancy change as age increases based on this table?
5. Can you provide a real-world example where life expectancy calculations are essential?

#### Tip:
When creating the Excel formulas, ensure that each calculation (for \( P_{x+j} \) and \( LE_x \)) is broken down into individual cells to allow easy modification if needed.

Create an Excel spreadsheet which computes life expectancies at ages x = 0, 40, and 80 using data from a life table for Male Survivors. Calculate the corresponding expected ages at death and paste your Excel work into a detailed report.

Learn how to calculate life expectancy at ages 0, 40, and 80 using a Male Survivors life table. This problem involves survival probability calculations and computing the expected age at death based on survival analysis. Suitable for university-level courses in actuarial science and demographics.

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