A textbook on probability and statistics

In summary, probability deals with predicting future events while statistics analyzes and interprets past data. Real-life applications include finance and understanding these concepts is important for making informed decisions. The central limit theorem is crucial in statistics and common misconceptions include equating low probability with impossibility and assuming causation from correlation.
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Hello, a very interesting forum you have here:)
So, to business
The topic says it all - I'm looking for a good textbook for undergraduate on probabilities and mathematical statistics. Could you recommend something?

I thought about: First Course in Probability by Sheldon Ross, but I have read a lot of bad reviews about that book, so I think it's out of the game.
 
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I like
Probability and Random Processes, Third Edition, by Grimmett and Stirzacker, (Oxford University Press, 2001).
 

1. What is the difference between probability and statistics?

The main difference between probability and statistics is that probability deals with predicting the likelihood of a future event occurring based on known information, while statistics deals with analyzing and interpreting data from past events to make inferences and conclusions about a population.

2. Can you give an example of a real-life application of probability and statistics?

One example is in the field of finance, where probability is used to predict stock market trends and statistics is used to analyze and interpret economic data to make investment decisions.

3. What is the importance of understanding probability and statistics?

Understanding probability and statistics is crucial in making informed decisions in various fields such as business, science, and medicine. It helps us make predictions, identify patterns, and draw meaningful conclusions from data.

4. How does the central limit theorem relate to probability and statistics?

The central limit theorem states that as the sample size increases, the sampling distribution of the mean will approach a normal distribution. This is important in statistics because it allows us to make inferences about a population based on a sample, assuming the sample is large enough.

5. What are some common misconceptions about probability and statistics?

One common misconception is that a low probability event is impossible, when in reality, it is just less likely to occur. Another misconception is that correlation implies causation, when in fact, there may be other factors at play and correlation does not necessarily indicate a cause-effect relationship.

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