A First Course In Probability

By A. Bayer. 2016

673 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Slow and Stale Gradients Can Win the Race: Error-Runtime Trade-offs in Distributed SGD (2018, neutral): “Xi ∼ exp(μ) is E [XP :P ] = ∑P i=1 1 iμ ≈ logP μ [Sheldon, 2002].”
Topology optimization of continuum structures with stress constraints and uncertainties in loading (2018, unknown): “ρ (l) e ← ρ (b+1) e − k2 ( ρ (b) e − ρ (l) e ) , (45)”
A modern introduction to probability and statistics (2026, unknown): “For example, for applications it is interesting that it is not necessary that all Xi have the same distribution; see Ross [26], Section 8.”
Maximum likelihood estimation of a spatial autoregressive Tobit model (2015, unknown): “(ii) Notice [(In −GnAnGn)−1GnAnGn]lii = l∏ j=1 ∞∑ Lj=1 [GnAnGn] Lj ii = ∞∑ k=l ∑ L1+L2+···+Ll=k [GnAnGn] k ii = ∞∑ k=l k + l − 1 l − 1 gi,kn 6 ∞∑ k=l (k + l − 1)l−1gi,kn, (B.5) where the third equality follows from Sheldon (2002).”
Equalization matching of speech recordings in real-world environments (2016, methodology): “Our best guess is to compute the filter G as the ratio: G(ω) = Ya(ω)/Yb(ω) (8)”
Three tutorial lectures on entropy and counting (2014, background): “The author first saw this proposition in Ross’s undergraduate textbook [53], but it is undoubtedly older than this.”
On the Delay-Storage Trade-Off in Content Download from Coded Distributed Storage Systems (2013, methodology): “It is more efficient to use coding instead of replication.”