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$t^5 - 6t + 3 = 0$


2d
answered Independent events and Kolmogorov
2d
comment How to find $\lim\limits_{n\to \infty }(1 + \frac{1}{n})^n$
@PedroTamaroff Yeah, it's not very beautiful, but when I use the small format it's a bit illegible, so I prefer being ugly but clear...
2d
revised How to find $\lim\limits_{n\to \infty }(1 + \frac{1}{n})^n$
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2d
answered How to find $\lim\limits_{n\to \infty }(1 + \frac{1}{n})^n$
2d
revised In Markov chains a limit distribution is invariant
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2d
answered Show that $P(X > \lambda) \geq \frac{(EX - \lambda)^2}{EX^2}$
2d
answered In Markov chains a limit distribution is invariant
2d
comment Convergence a.e. of the series $\sum_{i=1}^{n^2} \frac{X_i}{n^2}$
The trick is: if $\sum_{n=1}^\infty P(|Y_n - Y| >\epsilon)< \infty$ for all $\epsilon >0$, then $Y_n \to Y$ almost surely
2d
answered Convergence a.e. of the series $\sum_{i=1}^{n^2} \frac{X_i}{n^2}$
Jan
27
reviewed Leave Open To find the total no. of six digit numbers that can be formed having property that every succeeding digit is greater than preceding digit.
Jan
27
comment Find the Probability random walks hits $b$ before $c$ before $a$
I think $p=q$ does not change much, difference equations can still work
Jan
27
comment Find the Probability random walks hits $b$ before $c$ before $a$
yes, or we can apply martingale technique, both will work.
Jan
27
comment Find the Probability random walks hits $b$ before $c$ before $a$
By Markov property, $P_0(\tau_b < \tau_c < \tau_a) = P_0(\tau_b < \tau_c)P_b(\tau_c < \tau_a)$
Jan
27
comment $\frac{S_n}{n} \to -1 \ \ a.e.$, exercise from probability book
You are faster, +1
Jan
27
comment Is $2^{xy}$ a positive definite kernel?
You want the positivity of generalized Vandermonde matrix, see this MO post
Jan
27
comment Determining corners of this convex set
yeah, this may be easier to answer
Jan
27
comment Determining corners of this convex set
By Krein–Milman theorem, $P$ is the convex hull of its extreme points
Jan
27
reviewed Leave Open Studying math all day and really young
Jan
27
reviewed Leave Open Interval of convergence of the series $\sum\limits_{m=1}^{\infty}x^{\ln (m)}$
Jan
27
answered Calculation of a characteristic function