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5.6147 bits
Each probability is 1/49. Hence H = −49(1/49)log₂(1/49) = log₂(49).
5.6724 bits
Each probability is 1/51. Hence H = −51(1/51)log₂(1/51) = log₂(51).
2.3219 bits
Each probability is 1/5. Hence H = −5(1/5)log₂(1/5) = log₂(5).
State the logarithm base; base 2 gives bits. The probabilities sum to one.
Advanced universityState the logarithm base; base 2 gives bits. The probabilities sum to one.
Advanced universityPractise improper integrals, series, gradients and multiple integrals, with explicit conditions and worked examples.
Develop matrix, vector-space and projection reasoning before using least squares.
Connect initial conditions, linear differential equations and numerical approximation with error and conditioning.
Work with conditional probability, normalization, densities and expectation.
Build epsilon proofs and distinguish pointwise convergence, uniform convergence and compactness.
Study groups, vector-space quotients and proof techniques with carefully scoped definitions.
Study complex analysis, residues, Fourier series, PDE boundary conditions and convexity through focused lessons.
Learn descriptive statistics, probability, sampling and inference with worked reasoning.