O Find the moment generating function of X = -cY. ) What is the distribution of X?
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- If X, Y are normally distributed independent random variables, then show that W = 2X - Y is normally distributed. Do not use moment generating function, only use convolution formula.Suppose Y is a continuous random variable drawn from the uniform distributionon the interval [3, 4], that is, Y ∼ Uniform([3, 4]). Conditioned on Y = y, a second randomvariable X is drawn from the uniform distribution on the interval [0, y]. What is fX(x), thepdf of X?Let Y1, Y2, ... , Yn be a random sample of size n from a gamma distribution with parameters α = 1and β = 2. Derive the probability distribution of the sample mean Y̅ using moment-generatingfunctions.
- If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?Let X1, X2, ... Xn random variables be independent random variables with a Poisson distribution whose parameters are l1, l2, ... ln, respectively. Which of the following is the moment generating function of the random variable Z defined as (the little image)?If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.
- Suppose that random variable X is uniformly distributed over the interval (0,1). Assume that the conditional distribution of Y given X=x has a binomial distribution with parameters n and p=x. Find E(Y).If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recorded