5. Show that for the distribution df = yo e¯x/2 " – 1 dx, 0sxs∞ n-1 n + Hj' (about the origin) = v2r and µ2' = n. %3D
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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.Consider the joint PDF f(x,y)=4xy for 0<x<1 and 0<y<1. (a) Are X and Y independent?(b) Find both marginal distributions. (c) Find both conditional distributions.
- suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)If X is an exponential random variables with rate 1, then its distribution function is given by F(x) = 1 − e−x Show that x = − ln(1 − u).In a t-distribution, what is the area under the curve that is to the right of t=2.048 and with df=28? (Show solution)
- In a t-distribution, what is the area under the curve that is to the right of t=2.048 and with df=28?For c in R, calculate E[e^cX] where X is exponential distribution.Find the mean and variance of the gamma distributionusing integration to obtain E(X) and E(X2).[Hint: Express the integrand in terms of a gammadensity.]
- Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?2 Given the exponential distribution: f(x) = {1/θ e^(-x/θ) ; x > 0 0; ew]Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?
