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 Sep30 awarded Explainer Sep28 comment Relationship between 2 L-p spaces Hint: (1) use that $f$ is bounded, (2) prove that for every bounded $f$, there exists $C$ such that $|f(x)|^{p_2} \leq C |f(x)|^{p_1}$ for every $x$. Sep28 comment Relationship between 2 L-p spaces For this statement to be true, we should have $p_1 \leq p_2$. Sep28 comment Relationship between 2 L-p spaces This is false if $f$ is bounded and $\mu(E) = \infty$. Consider $f(x) = 1$. We have, $f\in L_{p_1}({\mathbb R})$ for $p_1=\infty$, but $f\notin L_{p_2}({\mathbb R})$ for $p_2 = 1 Q -> R as P -> (Q -> R).” Mar16 comment Difference between$A\to B\to C$and$A\to(B\to C)$See e.g. springer.com/cda/content/document/cda_downloaddocument/… : “Although the implication operator is assumed to be right associative, so that$p \to q \to r$unambiguously means$p \to (q \to r)$, we will write the formula with parentheses to avoid confusion with$(p\to q)\to r$.” Mar16 answered Difference between$A\to B\to C$and$A\to(B\to C)$Mar16 revised On the importance of independence in the central limit theorem added 187 characters in body Mar16 answered On the importance of independence in the central limit theorem Feb18 revised Estimating certain order statistics of a set. added the normalization factor k/n to the formula for E[Y] Feb18 answered Estimating certain order statistics of a set. Feb1 reviewed Approve Prove that$\sum_{k=1}^{n}\binom{n}{k}=\sum_{k=0}^{n-1}2^{k}$Feb1 comment Random walk on$\mathbb{Z}$with more than two possible steps Sounds good. Regarding question 2, even if$A=\{-1,1\}$and$p_{-1} > p_1$, we have$\lambda_1=1$and$\lambda_2 > 1$. Consider another example:$A=\{-3,-1,2\}$and$p_{-3} = 1/4$,$p_{-1} = 1/4$, and$p_2 = 1/2$. Then values of$\lambda$are given by$\lambda^{-2}/2 + \lambda/4 + \lambda^3/4 = 1$. The roots of this equation have absolute values approximately 1, 0.6388969200, and 1.769292354 (some are equal to 1, some are greater than 1, and some are less than 1). Feb1 comment Random walk on$\mathbb{Z}$with more than two possible steps (1) I don't understand your formula. What is the event$a=-1$? When does it happen? (2) The expression$A \lambda_1^k + B \lambda_2^k$is unbounded (either when$k > 0$, or$k < 0$, or both) unless$A \lambda_1^k + B \lambda_2^k \equiv 1$. Feb1 comment Random walk on$\mathbb{Z}$with more than two possible steps How did you get the recurrence relation? The random walk might visit point$k-1$many times; each time it visits$k-1$, there is a chance that it will go to point$k$. Also is$k$a positive integer? If not, your formula might give values greater than 1 for$\tilde p_k$(which doesn't make any sense). Jan28 answered A random variable with neither probability density function nor probability mass function… is this example wrong? Jan27 awarded Enlightened Jan27 awarded Nice Answer Jan24 answered Why is$E(X^2)$not equal to the sum of$(x^2 \cdot P(x^2))$instead of$x^2 \cdot P(x)\$