Reasoning in "Prove $X$ is a martingale" / Different approach using indicator functions
42143
Prove X is a martingale
67452
Prove sum of unindependent Gaussian random variable is still Gaussian
66996
Proof by induction of Bernoulli's inequality $ (1+x)^n \ge 1+nx$
145136
When can we interchange the derivative with an expectation?
92569
Showing that ${\rm E}[X]=\sum_{k=0}^\infty P(X>k)$ for a discrete random variable
139342
$L^p$ submartingale convergence theorem
153538
Proving Holder's inequality using Jensen's inequality
45143
Identify $E(X\mid X+Y)$ for $X$ and $Y$ independent and Poisson
132920
Help with proof that the expected value of $x_i$ is $\bar{X}$
134696
How can I show that the conditional expectation $E(X\mid X)=X$?
38785
Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$
148790
Basic question about proofs with the goal $\exists x P(x)$
99165
How to prove that for Brownian motion in $(a, b)$ $\mathbb{E}^x[\min(H_a, H_b)] = (x-a)(b-x)$?
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
79794
Prove the time inversion formula is brownian motion
136694
Probabilistic Proof of Kraft-Mcmillan Inequality
40420
Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$