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Perform each operation.
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ALEKS 360 ACCESS CODE- PATHWAY MATH LIT
- 1. Sketch the following sets and determine which are domains: (a) |z−2+i| ≤ 1; - (c) Imz> 1; (e) 0≤ arg z≤ л/4 (z ± 0); Ans. (b), (c) are domains. (b) |2z+3| > 4; (d) Im z = 1; - (f) | z − 4| ≥ |z.arrow_forward8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward
- 9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward
- So let's see, the first one is the first one, and the second one is based on the first one!!arrow_forward1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward4. In each case, sketch the closure of the set: (a) -л 0.arrow_forward
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