Let X be a continuous random variable whose probability density function is: f(x) = x3/4; 0<x<2 a.Calculate E(X2). b. Calculate the standard deviation of X. c. c. Calculate P(X>0.5).
Added by Luis Miguel M.
Step 1
To calculate E(X^2), we need to find the integral of x^2 * f(x) from 0 to 2: E(X^2) = ∫[x^2 * (x^3/4)] dx from 0 to 2 E(X^2) = ∫[x^(5/4)] dx from 0 to 2 Now, we integrate: E(X^2) = (4/9)x^(9/4) | from 0 to 2 E(X^2) = (4/9)(2^(9/4)) - (4/9)(0^(9/4)) E(X^2) = Show more…
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