A Level Mathematics S2 Revision Notes

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Continuous Random Variables

- A continuous random variable is the integral of a PDF, for example if we have a PDF of 2x, we would have a continuous random variable of x^2.

- This is used in Cumulative Distiribution Functions (CDF) a lot, as CDFs are worked out by integrating the PDF, putting in the limits for the area we want to find the probability of a given range.

E(x) and Var(x)

For the Expected value, the formula is the same for working out the CDF, except the bottom limit is 0 and the upper limit is your highest value for (x)

For Variance, the usual formula applies: Var(x) = E(x^2) - [E(x)]^2

Approximations

-Binomial to Poisson- Needs: Large number of trials, small probability ,eg: X~B(200,0.1)

Method: X~Po({number of trials}*{probability})

-Binomial to normal- Needs: Large amount of trials, probability close to 0.5, eg: X~B(300, 0.49)

Method: X~N({np},{npq**})

• • remember that this is the variance; for the standard deviation you want to square root this number

Estimation and Sampling

Hypothesis Testing