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Probability: Difference between revisions
→Normal + Normal
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This is important for tests.<br> | This is important for tests.<br> | ||
See [https://en.wikipedia.org/wiki/Relationships_among_probability_distributions Relationships among probability distributions]. | See [https://en.wikipedia.org/wiki/Relationships_among_probability_distributions Relationships among probability distributions]. | ||
===Normal | ===Normal Distributions=== | ||
If <math>X_1 \sim N(\mu_1, \sigma_1^2)</math> and <math>X_2 \sim N(\mu_2, \sigma_2^2)</math> then <math>\lambda_1 X_1 + \lambda_2 X_2 \sim N(\lambda_1 \mu_1 + \lambda_2 X_2, \lambda_1^2 \sigma_1^2 + \lambda_2^2 + \sigma_2^2)</math> for any <math>\lambda_1, \lambda_2 \in \mathbb{R}</math> | If <math>X_1 \sim N(\mu_1, \sigma_1^2)</math> and <math>X_2 \sim N(\mu_2, \sigma_2^2)</math> then <math>\lambda_1 X_1 + \lambda_2 X_2 \sim N(\lambda_1 \mu_1 + \lambda_2 X_2, \lambda_1^2 \sigma_1^2 + \lambda_2^2 + \sigma_2^2)</math> for any <math>\lambda_1, \lambda_2 \in \mathbb{R}</math> | ||