# Pdf Let X1, X2,..., X, be a random sample from the Pareto distribut.docx

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pdf: Let X1, X2,..., X, be a random sample from the Pareto distribution with parameter 7. Investigate the convergence in distribution of Yn := n ln(X (1) + 1) where X (1) = min(X1, X2,...,xn). Name Parametric Families of Continuous Distributions pdf = f(x) Parameter Mean Space Variance cdf = F(x) -00 < a < 0 f(*) = 110,0+B)(2) a + > 0 -00< (1-1) f(x) = < 00 oo f(x) = le-210,00) (2) 0 < X < oo Moment Generating Function = E[ex] ela+8)+ -eat At Uniform Normal exp[ut + 3024] Exponential (rate ) Bilateral exponential for t < eta /(1 - t/B2) for t < 8 Be-B|z-a! f(x) = --o0<a < 00 0 < < OO cx > 0 B >O Gamma f(x) = r Baza-1e-(B2) (0,00) () Weibull f(x) = 3 (5")*6-64)' I10.00,(3) 69 50 Ja+Br(1+ B  Unformatted text preview: I (1+2 -p? (1 + 5 � for t &lt; 8 not useful E[(X - a)*] = Br(1+ not useful EX= Bla+k,b) Bla,b) does not exist Beta f(0) = \$12.17 24-(1 2 ) � 4:10.1) (7) a &gt; 0 b&gt;0 (a+b)2(a+b+1) Pareto 7 &gt; 0 1/(1-1) � for 7 &gt; 1 does not exist 7/167-2)(-1)) for y&gt; 2 0 Cauchy does not exist does not exist f(x) = (1+)*+1 110,00) (2) f(t) = BIS F(x) = (1 + e-(79)) f(x) = exp(-e-() -00&lt;a &lt; B&gt;0 - &lt; a &lt; B&gt;0 0 Logistic I B22/3 eat csc() - Gumbel (Extreme value) &lt;a &lt; 8 &gt; 0 at By where 0.577216 B 7 /6 eatr(1 - Bt) for t &lt; 1/8 y � �-o0&lt; &lt; OO Log normal F(x)= 0 (-) (0,00)(x) exp[2 + 20P] exp[2 + 204)- exp[2 + 0] does not exist EX = exp[ku + R202)...
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