HW6key3

.pdf
School
Arizona State University **We aren't endorsed by this school
Course
EEE 304
Subject
Statistics
Date
Aug 31, 2023
Pages
1
Uploaded by BarristerVulture3269 on coursehero.com
To use a central limit theorem approximation, we find the expected value and variance of X . E [ X ] = E [ V 1 ] + E [ V 2 ] + · · · + E [ V 30 ] 6 = 5 E [ V ] = 100 . (3) Since the V i are iid, Var[ X ] = Var[ V 1 + · · · + V 30 ] 36 = Var[ V 1 ] + · · · + Var[ V 30 ] 36 = 30 36 Var[ V ] = 250 21 . (4) Since X is a sum of 30 iid random variables, it is reasonable to make the central limit theorem approximation P [ X 95] = P " X - E [ X ] p Var[ X ] 95 - E [ X ] p Var[ X ] # P " Z 95 - 100 p 250 / 21 # = Q - r 21 10 ! = Φ( 2 . 1) = 0 . 9264 . (5) 2
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