[コンプリート!] Vp ¯^ Y bNXȵ 120720
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Vp ¯^ Y bNXȵ
Vp ¯^ Y bNXȵ-> B ~ Ñ C C ª »8 v ¸ v>Û L ê8 ;?10 pts Solution The general formula for the density of a normal distribution with parameters µ and σ is f(x) = (1/ √ 2πσ)e−(x−µ)2/(2σ2) Here µ = 1, σ = √ 4 = 2, so f X(x) = 1 2 √ 2π exp (− 1 2 x−1 2 2), −∞ < x < ∞ (c) Let Y = eX Find the pdf f Y (y) of Y (Again, the
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Y / p G & ¯ L }7 è à Æ ¹ ñ µ ñ ® £ Ö ¢ s?Individuals applying for licensure for professions that require !Pa • X • b Note that if and X are discrete distributions, this condition reduces to P = xi!
1 ra ndom v ector with mean µ x and v aria nce co v ar iance ma trix !P V b { ¤ Ñ M v t 0 D ó q O z p þ a ¼ t x µ Õ µ Ä x °II Let x1, x2, , x n be a random sample drawn from a population with mean µ and variance σ2In other words, E(xi) = µ, and Var (xi) = σ 2 for i = 1, 2, , n, and the x’s are all independent of each otherLet ∑ n i xi n x 1 1 be the sample mean (a) (4 points) Show that E(x) = µE( x ) = E (∑n i xi n 1 1) = n 1 E(∑) = n i xi 1 n 1 ∑ n i E xi
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