Give algorithms for generating random variables from the following distributions.
b.
Give algorithms for generating random variables from the following distributions. b. 1-2 if 0<<1
Using the result of exercise 7(see question 7 below), give algorithms for generating random variables from the following distributions. b. 1-2 if 0<<1 7. (The Composition Method) Suppose it is relatively easy to generate random variables from any of the distributions F,,-I, . . . , n. How could we generate a random variable having the distribution function 12 i-1 where p,, -1.... . n, are nonnegative numbers whose sum is 1?
There are 30 people that donated to a church. The amount each person donated has probability density function Find out the probability that exactly 5 people donated between 20 and 30. ,(1)-(*(50-r), (50-x), ifo ifo < x < 50 otherwise TA
max{a1, a2, n<3 Show that 1 1 1 7 . 3 (a1a +.an) 3 an 3 a2 3- a1 using definition of convex
Consider a potential well, whose potential is given by (a) Evaluate the reflection and transmission coefficient for the case E > 0. (b) Use your result for the transmission coefficient obtained in (a) above, to evaluate the transmission coefficient for the potential barrier, (V0 > 0) for the case E < V0. Please show all steps thoroughly S-V, (-a <r <a) 10, elsewhere JV, (-a <r <a) V.C) = 0. elsewhere
The amount of kerosene, in thousands of litres, in a tank at the beginning of any day is a random amount Y from which a random amount X is sold during that day. Suppose that the tank is not resupplied during the day so that x y, and assume that the joint density function of these of these variables is Determine the correlation coefficient between X and Y and interpret the value calculated. We were unable to transcribe this imagef...
If X is a Poisson random variable with parameter ?, show that the Tchebyshev’s inequality will indicate P(0 < X < 21) >1–
Let f: a, b R be a function, continuous on a, b and differentiable on (a, b). Show that 3c E (a, b) such that f (b) f(c) <0 f (e) f(a) 3s E (a, b) s.t f'(s) 0.
0Let X1, ....., Xn be iid Random variable from a Uniform distribution with pdf given by . (1) Is the 2-dimensional statistics T1(X) = (X(1), X(n)) a complete sufficient statistics? Justify your answer (2) Is the one-dimensional statistic a complete sufficient statistic? Justify your answer We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let be the distribution function defined by Let be the Lebesgue-Stieltjes measure asociated to . Determine the measurements of the fpllowing sets: We were unable to transcribe this imageF(x) = 0 if 1+r if 2+x? if 19 if I <-1 -1 <r <0 0<r<2 > 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image(-1, 0]υ (1,2) 10, ) U (1, 2 (1 :...
(6) . We pick samples randomly from the population which distributes uniformly between the interval of. . Answer the following questions regarding the median of the samples Show that the distribution which follows has the distribution as shown below. Find the expected value of . Show = . When , show that is the consistent estimator of . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagen = 2m...