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It looks like you've uploaded an image with a set of probability and statistics exercises. I'll go over each task briefly and provide help where needed:

1. **Calculate Mean and Standard Deviation:**
   - (a) Data: \(1; 5; 3; 5; 2\) without GTR (technology).
   - (b) Data: \(2.2; 3.7; 0.1; 9.4; 1.1; 0.1\) with GTR.

2. **Mean and Standard Deviation for Frequency Distribution:**
   - Two tables provided, one for GTR (technology use) and one without. These require using frequency-weighted mean and standard deviation formulas.

3. **Spinning Wheel with Two Spins:**
   - The random variable \(X\) is the sum of the outcomes. You need to:
     - (a) Create a probability distribution for \(X\), draw the graph.
     - (b) Calculate \(P(X \geq 7)\).
     - (c) Calculate \(P(2 \leq X \leq 4)\).

4. **Expected Value and Standard Deviation for Task 3:**
   - Compute these using the distribution from Task 3.

5. **Simulate 100 Spins (from Task 3):**
   - Use the expected value and standard deviation of empirical data to compare with Task 4.

6. **Fairness of a Game:**
   - (a) The table shows different values of \(g\) (gain/loss). Check if the game is fair based on expected value.
   - (b) Adjust the win amount for \(g = 5\) to make the game fair.

7. **Binomial Probability:**
   - (a) Describe a situation where you use the binomial formula \(\binom{20}{4} \cdot 0.6^4 \cdot 0.4^{16}\).
   - (b/c) Calculate and interpret \(\binom{20}{4}\).

8. **Bernoulli Chain (Probability = \( \frac{1}{3} \)):**
   - Various tasks based on hitting probability.

9. **Red and Green Balls Problem:**
   - Use combinatorics to calculate different outcomes with 8 balls, mixing red and green.

10. **Number of Sixes in 45 Dice Rolls:**
    - Compute expected value and standard deviation for the number of sixes.

Would you like detailed solutions for any of these tasks, or for a specific problem? Let me know which you'd prefer!

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Here are some related questions:

1. How is the standard deviation formula applied to frequency distributions?
2. What methods can be used to calculate the probability distribution for Task 3?
3. How do you verify if a game is fair using expected value?
4. What is the binomial coefficient and how is it used in probability?
5. How do Bernoulli processes apply to real-world probability problems?

**Tip:** Remember, for calculating standard deviation, it's essential to keep track of whether you're using sample or population data, as the formulas slightly differ.

A set of probability and statistics exercises including calculating mean, standard deviation, expected value, and solving Bernoulli and binomial problems.

Solve probability and statistics problems including calculating the mean, standard deviation, and expected value, with applications of Bernoulli and binomial probability formulas. Suitable for high school students (Grades 9-12).

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