be iid. random variables with expectation 1 and finite 34. Let X1, X, variance o2, and set S, = X1+X2 + +--+X,, for n21. Show that as n 0. and determine the constant 6.
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- Suppose an insect lays a very large number of eggs Y, where Y ~ Po(lambda), and suppose that each egg survives with probability p. Assuming that the egg's survival is independent, on the average, how many eggs will survive?Suppose that Z1, Z2, . . . , Zn are statistically independent random variables. Define Y as the sum of squares of these random variablesLet X1, X2, ... Xn random variables be independent random variables with a Poisson distribution whose parameters are l1, l2, ... ln, respectively. Which of the following is the moment generating function of the random variable Z defined as (the little image)?
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- Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?Suppose that after we arrive at a bus stop the time until the bus arrives is uniformly distributed in the interval 0 to 15 minutes. If we arrive at such a bus stop, find the probability that we must wait at most 10 minutes.