Let n e N, Let X1,.., Xn be independent and identically distributed random variables with well...

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Let n e N, Let X1,.., Xn be independent and identically distributed random variables with well defined expectations and variances satisfying u = E[X;] and o2 = Var (X;) > 0. Set Sn = X1+ .. +Xn. For the following list of statements, select those statements which are true: For any t e R Sn-nu P (t) limn→00 For any t e R limno P Sn-пи <t (t) ovn For any t E R (누리 Sn-H limn→00 P 2t) = (t) For any t e R Sn-nu ovn 21) = #(t) limn→00 P For any t e R Sn-nu <t) = #(t) limn00 P In a factory making electronics, products on a production line are defective with probability 1/5, independently of each other. Let X be the random variable determined by the total number of products that are made until the first defective product is discovered. 1. Select which of the following distributions X follows O X~ bin2,1/5 o X- bing,1/10 O X- Geo(1/10) O X- Geo(1/5) 2. O X~ Geo(2/5) O X~ N(2,1/10) O X~ N(2,1/5) O X~ N(2,2/5) Let n e N, Let X1,.., Xn be independent and identically distributed random variables with well defined expectations and variances satisfying u = E[X;] and o2 = Var (X;) > 0. Set Sn = X1+ .. +Xn. For the following list of statements, select those statements which are true: For any t e R Sn-nu P (t) limn→00 For any t e R limno P Sn-пи <t (t) ovn For any t E R (누리 Sn-H limn→00 P 2t) = (t) For any t e R Sn-nu ovn 21) = #(t) limn→00 P For any t e R Sn-nu <t) = #(t) limn00 P In a factory making electronics, products on a production line are defective with probability 1/5, independently of each other. Let X be the random variable determined by the total number of products that are made until the first defective product is discovered. 1. Select which of the following distributions X follows O X~ bin2,1/5 o X- bing,1/10 O X- Geo(1/10) O X- Geo(1/5) 2. O X~ Geo(2/5) O X~ N(2,1/10) O X~ N(2,1/5) O X~ N(2,2/5)