3. For the probability density function of a random variable X, based on a parameter € > 0 c(0) (0²-x²) 0 for-0≤x≤0, otherwise. (a) Find c(0). fx(x|0) = (b) Find the second moment, 2 = EX². (c) Note that the mean µ = EX = 0 for all values of 0. Use the second moment to find a method of momento potimoto Af

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3. For the probability density function of a random variable X, based on a parameter € > 0
£x (2|0) = { 0(0) (0² – x²)
(a) Find c(0).
(b) Find the second moment, µ2 = EX².
for-0≤x≤0,
otherwise.
(c) Note that the mean µ = EX = 0 for all values of 0. Use the second moment to find a method of
moments estimate for based on data x₁, x2, ..., Xn.
Transcribed Image Text:3. For the probability density function of a random variable X, based on a parameter € > 0 £x (2|0) = { 0(0) (0² – x²) (a) Find c(0). (b) Find the second moment, µ2 = EX². for-0≤x≤0, otherwise. (c) Note that the mean µ = EX = 0 for all values of 0. Use the second moment to find a method of moments estimate for based on data x₁, x2, ..., Xn.
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