= Jonathan Bloom
{c}
\b[Jonathan Bloom] is a mathematician and teacher identified by MIT's Experimental Study Group with work in <topology> and redevelopment of the probability-and-statistics course 18.05. Its institutional profile connects those activities to his later computational research.<Jonathan Bloom profile by MIT Experimental Study Group>[Institutional biography, topology work and redevelopment of 18.05]{ref}
Bloom and <Jeremy Orloff> are named coauthors of <Covariance and Correlation by Jeremy Orloff and Jonathan Bloom>. The reading defines <covariance> and <correlation> and derives their basic properties.<Covariance and Correlation by Jeremy Orloff and Jonathan Bloom>[First-page byline; Sections 2–3]{ref} This documented teaching contribution offers a precise mathematical example of separating a definition from a stronger conclusion that it does not imply.
For an original example, let a <random variable> $X$ take values $-1,0,1$ with equal probabilities and set $Y=X^2$. Then
$$
\mathbb EX=0,\qquad \mathbb EY=\frac23,\qquad
\mathbb E[XY]=\mathbb E[X^3]=0,
$$
so $\operatorname{Cov}(X,Y)=0$. Both variances are positive:
$$
\operatorname{Var}(X)=\frac23,\qquad
\operatorname{Var}(Y)=\frac29,
$$
and their <correlation coefficient> is zero. Nevertheless they are not <independent random variables>, because
$$
P(Y=0\mid X=0)=1\ne P(Y=0)=\frac13.
$$
The pair consists of <uncorrelated random variables> with exact nonlinear dependence.
This calculation explains why a covariance summary can miss a deterministic relation; it is not an empirical dataset or a claim that Bloom originated the distinction. Connecting formal properties to counterexamples is directly useful when mathematical statistics is applied to complicated data. The institutional biography documents Bloom's movement between mathematical teaching and computational work, while the named course source supplies the concrete authored contribution.
Back to article page
