a sequence of random variables X1, X2, .... Suppose X, follows a discrete distri- bution taking two possible values {0, n²}, with P(X, = 0) = 1 – and P(X, = n²) =. Calculate E(Xn). What happens to E(X„) as n → 0? Does X, converge in probability to some real number? If so, find that number and prove. If not, explain.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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a sequence of random variables X1, X2, . ... Suppose X, follows a discrete distri-
bution taking two possible values {0, n²}, with P(X, = 0) = 1 – 1 and P(X, = n²) = !.
Calculate E(X„). What happens to E(X) as n → ∞?
Does X, converge in probability to some real number? If so, find that number
and prove. If not, explain.
Transcribed Image Text:a sequence of random variables X1, X2, . ... Suppose X, follows a discrete distri- bution taking two possible values {0, n²}, with P(X, = 0) = 1 – 1 and P(X, = n²) = !. Calculate E(X„). What happens to E(X) as n → ∞? Does X, converge in probability to some real number? If so, find that number and prove. If not, explain.
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