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The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value.

2 votes
1 answer
227 views

Expected value of random walk

Consider a random walk with $S_n=\sum^n_{i=1}X_i$, where the random i.i.d. steps $X_i$ take values $-1,0,2$ with probabilities $1/9,1/9,7/9$ respectively. Set $S_0=1$. I would like to calculate $E(S_n …
Slim Shady's user avatar
0 votes
0 answers
161 views

Termination of the random walk

Consider a random walk with $S_n=\sum^n_{i=1}X_i$, where the random i.i.d. steps $X_i$ take values $-1,0,2$ with probabilities $1/9,1/9,7/9$ respectively. Set $S_0=1$. The walk terminated whenever it …
Slim Shady's user avatar
6 votes
1 answer
248 views

True Error in Machine Learning

I have read this question and I am confused by a part of the first answer, even though it is asked in the comments. I don't understand why $$L_{(\mathcal{D}, f)}(h^{*}) = 0 \implies L_{S}(h^{*}) = 0$$ …
Slim Shady's user avatar