## Question 1: Descriptive Statistics for Tribe Data

**Problem Description:
**

Analyze the dataset 'tribe.RData' containing height and weight information.

**Mean height:**167.8419 cm**Mean weight:**64.5607 kg**Median height:**168.115 cm**Standard deviation of height:**7.068682 cm**Standard deviation of weight:**11.88245 kg**Correlation between weight and height:**0.1949294

## Question 2: Correlation Analysis of Midterm and Final Exam Grades

**Problem Description:
**

Examine the dataset 'grades.csv' with information about midterm and final exam grades.

**Sample size:**73 students**Correlation for all students:**0.6701399**Correlation for a subset of 30 students:**0.2593948**Explanation:**The correlation in part (e) is smaller due to the reduction in sample size. With a larger sample, the correlation approaches the population correlation coefficient.

## Question 3: Frequentist vs Bayesian Perspectives on Probability

**Problem Description:
**

Discuss the differences between the frequentist and Bayesian perspectives on the definition of probability.

**Frequentists see probability as relative frequency:**Bayesians view it as a function of belief.**Frequentists rely on experiments:**Bayesians use prior knowledge.**Frequentists treat parameters as fixed:**Bayesians treat them as random variables.

## Question 4: Sample Space of an Experiment

**Problem Description:
**

List all elements in the sample space of an experiment.

**Sample space:**{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

## Question 5: Meal Combinations

**Problem Description:
**

Calculate the number of meal combinations possible.

**Number of salads:**2**Number of main dishes:**4**Number of desserts:**3**Number of meal combinations:**24

## Question 6: Arrangement of Letters in a Word

**Problem Description:
**

Calculate the ways the letters of the word "CATHY" can be arranged.

**Ways to arrange:**120

## Question 7: Number of Different Committees

**Problem Description:
**

Calculate the number of different committees possible.

**Number of committees:**1,140

## Question 8: Committees with Women and Men

**Problem Description:
**

Calculate the number of different committees consisting of 2 women and 3 men.

**Number of committees:**350

## Question 9: Combinations Symmetry

**Problem Description:
**

Explain why (n¦r) = (n¦(n-r)).

- Whenever r items are selected, n−r items are left over. Hence the number of combinations of n things taken r at a time is equal to the number of combinations of n things taken (n-r) at a time.

## Question 10: Conditional Probability

**Problem Description:
**

Calculate conditional probabilities for coin-flipping events.

**P(A│B):**1/2**P(A│C):**1/3

## Question 11: Probability of Correct Guessing

**Problem Description:
**

Calculate the probability of correctly guessing four milk-first cups out of eight.

**Probability:**1 in 70 or 1.4%

## Question 12: Coin Flipping Probability

**Problem Description:
**

Calculate the probability of getting all heads when flipping four fair coins.

**Probability:**1/16