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Additional notes on random variables

The Law of Large Numbers ensures that the average results from multiple independent observations become predictable and approach the distribution mean. Statistical estimation accuracy relies on having sufficient observations. Discover rules for calculating means and variances of random variables.

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Additional notes on random variables

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  1. Additional notes on random variables

  2. Law of Large Numbers • The average results of many independent observations are stable and predictable. • The average of the values of X observed in many trials must approach . • Similar to probability…. In the long run, the proportion of outcomes taking any value gets close to the probability of that value, and the average outcome gets close to the distribution mean. • It assures us that statistical estimation will be accurate if we can afford enough observations. • Note: Insurance companies rely on this.

  3. Rules for means • If X is a random variable and a and b are fixed number, then • If X and Y are random variables, then • See examples on Page 327

  4. Rules for Variances • If X is a random variable and a and b are fixed numbers, then • If X and Y are independent random variables, then Addition Rule for variances of independent random variables. • If X and Y have correlation , then • General Addition Rule for variances of random variables.

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