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Let X be a random variable with PDF given by fX(x)={ c x^2 |x| ≤ 1 0 otherwise .a. Find the constant c.b. Find E X and Var(X).c. Find P(X ≥(1)/(2)).
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Let the random variable X have the pdf f(x ; θ)=(1 / θ) e^-x / θ, 0<x<∞, zero elsewhere. Consider the simple hypothesis H0: θ=θ^'=2 and the alternative hypothesis H1: θ=θ^''=4. Let X1, X2 denote a random sample of size 2 from this distribution. Show that the best test of H0 against H1 may be carried out by use of the statistic X1+X2 | Numerade
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