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Let X1,X2, . . . be a sequence of independent identically distribute.pdf

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Let X1,X2, . . . be a sequence of independent identically distributed random variables with finite mean and variance. Show that the sequence Yn = Xn/n converges to zero, with probability 1. Solution Y1 = X1/1, Y2 = X2/2, Y3 = X3/3... Yn = Xn/n According to Levy\'s theorem, The independent random variables Sn = X1 ,.

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Let X1,X2, . . . be a sequence of independent identically distributed random variables with finite mean and variance. Show that the sequence Yn = Xn/n converges to zero, with probability 1. Solution Y1 = X1/1, Y2 = X2/2, Y3 = X3/3... Yn = Xn/n According to Levy's theorem, The independent random variables Sn = X1 ,

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  • 1. Let X1,X2, . . . be a sequence of independent identically distributed random variables with finite mean and variance. Show that the sequence Yn = Xn/n converges to zero, with probability 1. Solution Y1 = X1/1, Y2 = X2/2, Y3 = X3/3... Yn = Xn/n According to Levy's theorem, The independent random variables Sn = X1 ,