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For a negative binomial random variable whose
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An Introduction to Mathematical Statistics and Its Applications (6th Edition)
- If we let RX(t) = ln MX(t), show that R X(0) = μ and RX(0) = σ2. Also, use these results to find the mean and the variance of a random variable X having the moment-generating function MX(t) = e4(et−1)arrow_forwardLet X be an exponential random variable with standard deviation σ. FindP(|X − E(X)| > kσ ) for k = 2, 3, 4, and compare the results to the boundsfrom Chebyshev’s inequality.arrow_forward1.9.5. Let a random variable $X$ of the continuous type have a pdf $f(x)$ whose graph is symmetric with respect to $x=c .$ If the mean value of $X$ exists, show that $E(X)=c$Hint: Show that $E(X-c)$ equals zero by writing $E(X-c)$ as the sum of two integrals: one from $-\infty$ to $c$ and the other from $c$ to $\infty .$ In the first, let $y=c-x$ and, in the second, $z=x-c .$ Finally, use the symmetry condition $f(c-y)=f(c+y)$ in the first.arrow_forward
- Find MAD for a continuous random variable with the given p.d.f. How does it compare with the standard deviation found in the earlier problem? The p.d.f. of a random variable X is f (x) = 2x for 0≤ x ≤1arrow_forwardQ1- What is the probability that the number of heads and are equal it a lait coin is tossed, a)15 times b)20 times Q2- Suppose the joint pdf of X and Y is given by: F xy (x y)={ ex +3y, if 0<x< 1 and 0<y<1 0 otherwise find E(x) . Q2- Suppose X is a random variable with E(X) = 5 and Var(X) = 2. What is E(X)?arrow_forwardConsider a random variable X with E[X] = 10, and X being positive. Estimate E[ln square root(X)] using Jensen’s inequality.arrow_forward
- For a random variable (X) having pdf given by: f(x) = (k)x^3 where 0 ≤ x ≤ 1, compute the following: a) k b) E(X). c) Var(X). d) P(X > 0.25).arrow_forwardThe pdf of a continuous random variable is defined as f(x)=8.75/x2 over (8.75, ∞) and 0 elsewhere. Find P( X > 65). (Round your answer to three decimal places).arrow_forwardA continuous random variable X has a pdf of the form: f(x) = (824/9) x^2, for 0.01 < X < 0.32. Calculate the standard deviation (sigma) of X.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage