Usé this to find the variance of X. 24. Assume that the increase in demand for electric power in millions– hours over the next 2 years in a particular area is a random var density is given by f(x) = (1/64)x³ 0

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Chapter10: Statistics
Section10.1: Measures Of Center
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Usé this to find the variance of X.
24. Assume that the increase in demand for electric power in millions–
hours over the next 2 years in a particular area is a random var
density is given by
f(x) = (1/64)x³
0<x<4
(a) Verify that this is a valid density.
. (b) Find the expression for the cumulative distribution for X, and
the probability that the demand will be at most 2 million kil
(e) If the area only has the capacity to generate an additional 3
watt hours, what is the probability that demand will exceed
(d) Find the average increase in demand. -
12
Tter
Section 4.3
25. Evaluate each of these integrals:
(a) o z?e-z dz
513V
(b) Jo zlez dz
m dx
(c) xe-x2
19m
wilided
(d) 0 (1/16)xex/4 dx
26. Prove Theorem 4.3.1. Hint: To prove part 1, evaluate I'(1) ở
definition of the gamma function. To prove part 2, use inte
with
Transcribed Image Text:Usé this to find the variance of X. 24. Assume that the increase in demand for electric power in millions– hours over the next 2 years in a particular area is a random var density is given by f(x) = (1/64)x³ 0<x<4 (a) Verify that this is a valid density. . (b) Find the expression for the cumulative distribution for X, and the probability that the demand will be at most 2 million kil (e) If the area only has the capacity to generate an additional 3 watt hours, what is the probability that demand will exceed (d) Find the average increase in demand. - 12 Tter Section 4.3 25. Evaluate each of these integrals: (a) o z?e-z dz 513V (b) Jo zlez dz m dx (c) xe-x2 19m wilided (d) 0 (1/16)xex/4 dx 26. Prove Theorem 4.3.1. Hint: To prove part 1, evaluate I'(1) ở definition of the gamma function. To prove part 2, use inte with
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