The time, in 100 hours, that a student uses her game console over a year is a random variable X with probability density function x if 0 < x < 1 f(x) = { 2 – x if 1 < x < 2 O otherwise. The power (in number of kilowatt hours) expended by the student's game console each year is 48X² + 26. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the mean amount of power expended by the student's game console per year. Part b)

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The time, in 100 hours, that a student uses her game console over a year is a random variable X with probability density function
( if 0 < х < 1
2 — ӕ if 1 < х <2
0 otherwise.
f(x) =
The
power (in number of kilowatt hours) expended by the student's game console each year is 48X² + 26. For these problems,
please ensure your answers are accurate to within 3 decimals.
Part a)
Find the mean amount of power expended by the student's game console per year.
Part b)
Find the variance of power expended by the student's game console per year.
Transcribed Image Text:The time, in 100 hours, that a student uses her game console over a year is a random variable X with probability density function ( if 0 < х < 1 2 — ӕ if 1 < х <2 0 otherwise. f(x) = The power (in number of kilowatt hours) expended by the student's game console each year is 48X² + 26. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the mean amount of power expended by the student's game console per year. Part b) Find the variance of power expended by the student's game console per year.
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