Probability distribution pitfalls: Avoiding errors in H2 math questions

Probability distribution pitfalls: Avoiding errors in H2 math questions

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Frequently Asked Questions

Forgetting to ensure that the sum of all probabilities equals 1. Always verify ΣP(x) = 1 for discrete distributions and ∫f(x) dx = 1 for continuous distributions.
Ensure you understand the probability density function (PDF) and cumulative distribution function (CDF). Remember that the area under the PDF curve represents probability, and the CDF gives the probability of a value being less than or equal to a specific point.
Incorrectly assuming independence between trials. The binomial distribution requires that each trial is independent of the others.
Be careful when applying continuity correction, especially when approximating discrete distributions with the normal distribution. Use it when approximating a discrete distribution.
Confusing P(A|B) with P(B|A). Understand which event is the condition and which events probability youre trying to find.
Ensure you correctly multiply each possible value by its corresponding probability and sum the results. Double-check your calculations to avoid arithmetic errors.
Ensure you understand how to calculate marginal and conditional probabilities from the joint distribution. Double-check that the joint probabilities sum to one.
Forgetting to take the square root of the variance to obtain the standard deviation. Remember that standard deviation is in the same units as the random variable.
Verify that events occur randomly and independently and that the average rate of events is constant over the interval. Ensure the rate is for the correct time interval.