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Question
Let X be a continuous random variable with probability density function
`"f"_x(x) = {{:(2x",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
Find the expected value of X
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Solution
Let x be a continuous random variable.
In the probability density function,
Expected Value E(x) = `int_(-oo)^oo x"f"(x) "d"x`
Here E(x) = `int_0^1 x(2x) "d"x = int_0^1 2x^2 "d"x`
= `2[x^3/3]_0^1`
= `2/3[x^3]_0^1`
= `2/3 [1 - 0]`
= `2/3`
∴ E(x) = `2/3`
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