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</center><p>As a result, it is one of the most important probability distributions in statistics. The sum of the degrees is 6(3) + 6(4) + 7(6) = Thus the stationary probability of being on a corner is 3== 1=28, on an edge is 4== 1=21, and in the center is 6== 1= What fraction of the time will the robber be in the center tile Probability Cheat Sheet Distributions Unifrom Distribution notation U[a;b] cdf x a b a for x2[a;b] pdfb a for x2[a;b] expectation(a+ b) variance(b a)2 mgf etb eta t(b a) story: all intervals of the same length on the distribution’s support are equally probable. Gamma Distribution notation Gamma(k;) pdf kx 1e x (k) I x>0 (k Expectation and Moments of the Distribution In the following sections, we are going to keep the same notations as before and the formulas will be explicitly detailed for the discrete (D) and continuous (C) cases Discrete RVs. Probabilities assigned to various outcomes in S in turn determine probabilities associated with the values of any particular rv X. ass Fxn/Probability Distribution,(pmf):p(x) = P(X = x) = P(8wW: X(w) = x) Gives the probability of observing wW: X(w) = x The conditions p(x)and P all possi Normal Distribution Cheat Sheet. Let EX = µ and Var(X) = σIfdistribution) for large n √ n(X¯ −µ) = √ n[1 n Xn i=1 X i −µ] ≈ N(0,σ2) Plus the table for To normalize this degree sequence, we divide by its sum. The normal distribution is a continuous probability distribution that can be used to model a vast number of naturally occurring scenarios. The integral of a normal  with a distribution F(x). Probability Cheat Sheet Distributions Unifrom Distribution notation U[a;b] cdf x a b a for x2[a;b] pdfb a for x2[a;b] expectation(a+ b) variance(b a)2 mgf etb eta t(b a)  2) The Binomial Distribution converges to the Normal Distribution when n is large and p is close to We have μ= np and σ= np (1− p)) A Normally Distributed random  Under certain conditions, the binomial distribution is statistically very similar to the normal distribution. Examples of natural variables that follow the normal distribution are IQ scores, height As a result, the normal distribution can be used as an approximation for  Some authors use the term \normal distribution" equivalently with \Gaussian dis-tribution". So, use the term \normal distribution" with caution.</p></translate>
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