Determine the transformation to generate binomial random variables with N = 3 and p = 0.3...
If I sum a binomial random variable with n=5 and p =0.3 and a binomial random variable with m=10 and p =0.5, I get Select one: a. Something unfamiliar to us as yet b. A normal distribution c. A binomial random variable with number of Bernoulli trials =15 and p =0.4 d. A Binomial with number of Bernoulli trials =15 and p=0.4
binomial RV B(n,p) 2. Simulating a Binomial RV. One procedure for generating uses n EXi is binomial if realizations of a uniform random variable and exploits the fact that Y the Xi are Bernoulli RVs. Here is an alternative procedure that requires generating only a single (!) uniform variate: 1/p and B 1/(1 p) 0) Let 1) Set 0 U[0, 1] 2) Generate 3) If k n, go to step 5; else, k ++ au; if u B(u- p). Go...
Let N be a binomial random variable with n = 2 trials and success probability p = 0.5. Let X and Y be uniform random variables on [0, 1] and that X, Y, N are mutually independent. Find the probability density function for Z = NXY.
Let X, Y be independent random variables where X is binomial(n = 4, p = 1/3) and Y is binomial(n = 3,p = 1/3). Find the moment-generating functions of the three random variables X, Y and X + Y . (You may look up the first two. The third follows from the first two and the behavior of moment-generating functions.) Now use the moment-generating function of X + Y to find the distribution of X + Y .
number2 how to solve it? Are x1 and x2 independent - yes, they are independent. Random variables X and Y having the joint density 1. 8 2)u(y 1)xy2 exp(4 2xy) fxy (x, y) ux- _ 3 1 1 Undergo a transformation T: 1 to generate new random variables Y -1. and Y2. Find the joint density of Y and Y2 X3)1/2 when X1 and X2 (XR 2. Determine the density of Y are joint Gaussian random variables with zero means...
Say I want to generate random variables from the probability distribution p={ 2-2x 0<x<1 0 . elsewhere My scheme is to generate U's from [0,1],double them and plug them into the probability distribution. So U = 0.3 gives me p(0.6)=0.8 as random variable. Prove my idea is right or wrong.
6. Imagine a negative binomial random variable X with p = 0.3 and r-3. (If you want to use R to determine the probabilities, be aware that the definition of a negative random variable is slightly different from the definition given in our text). Determine the following: a) E(X) b) V(X) c) P(X-20) d) P (X=19) e) P(X = 21)
Let X and Y be independent binomial random variables B(n,p) on the same sample space. Show that X + Y is also a binomial random variable B(?,?). What values should replace the questions marks?
6. Imagine a negative binomial random variable X with p 0.3 andr 3. (If you want to use R to determine the probabilities, be aware that the definition of a negative random variable is slightly different from the definition given in our text). Determine the following: a) E(X) b) V(X) c) P(X20) d) P(X=19) e) P(X=21)
5.a. Usining Binomial probability distribution formula for a random variable X, compute Where N= 15, p=0.3 and find P(x=2)? Begin P(X=2) =