Suppose {X,n} is a sequence of random variables draw from an underlying popu- lation space, then the sample mean of {Xn} defined as Xn = i-1Xi, converge in distribution to Normal Distribution N(u, o2), where u = E[X;], o2 Var[X 11 n (a) Randomly draw 10000000 samples from from N(20,25), plot the histogram of the samples and underlying population distribution together

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A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

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A: Let , where and

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A: The answer can be given using the concept of normal distribution.

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Q: The probability mass function of a discrete random variable is: 37-x A G for x = 1, 2, ., 14 (a)…

A: Solution-: We have, P(X)=a*(15)x(32)7-x   for x=1,2,3,.........14 We compute (a) P(3<X≤9)=? (b)…

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A: given  X~N5,2  the  z=X-μσ~N0, 1    mean = 5     variance = 2      ,   a) PX >2=PX-μσ>2-52…

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A: Z =(Xbar-mu)/sigma/sqrt(n) We want to find the probability P(X(1)>1/2)= ?  P(X(3)>1.5)= ?

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Q: The probability mass function of a discrete random variable is: 7-x p(x) = a(=) G) for x = 1,2, .,…

A: Solution-: We have the p.m.f. of a discrete random variable P(X=x)=a*(15)x*(32)7-x   for…

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A: It is an important part of statistics. It is widely used.

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A: As per guidelines of Bartleby, we have given solution of only first 3 parts

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Q: The probability mass function of a discrete random variable is: 7-x p(x) = a=) G) for x = 1,2,., 14…

A:

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