The Pareto random variable with parameters α >0 and β >0 has probability density function:
fX(x) = βα^β/[x^(β+1)], whereα < x < [infinity].
(a) Verify that fX is a density function.
(b) Find P{X > 2α}.
(c) Find the mean and variance of X. What restriction do you have on β in computing the mean and variance? Hint: There’s a different restriction on each.
(d) Use the probability transform to simulate 1000 Pareto random variables with α = 1 and β = 4 and find their sample mean and variance. Compare this to values in part (c).

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

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answer:   x = 3 + √11     and     x = 3 - √11

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x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

answer: answer: d) v= 1/6 bh  

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since according to the given question,   a pyramid is placed inside a prism.

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answer: what are the answer choices?

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