(6) (15 points) The moment generating function for a normal random variable N (17,0?) is given...
problem 3 and 4 please. 3. Find the moment generating function of the continuous random variable & such that i f(x) = { 2 sinx, Ox CT, no otherwise. 4. Let X and Y be independent random variables where X is exponentially distributed with parameter value and Y is uniformly distributed over the interval from 0 to 2. Find the PDF of X+Y.
Question 18: a) Compute the moment generating function, MGF, of a normal random variable X with mean µ and standard deviation σ. b) Use your MGF from part a) to find the mean and variance of X.
6. (4 marks) The moment generating function (mgf) of a random variable X is given by m(t)-e2 (a) Use the mgf to find the mean and variance of X (b) What is the probability that X-2?
(4 marks The moment generating function (mgf) of a random variable X is given by (a) Use the mgf to find the mean and variance of X (b) What is the probability that X = 2?
(3 marks) The moment generating function of a random variable X is given by MX(t) = 24 20 < - In 0.6. Find the mean and standard deviation of X using its moment generating function.
The moment generating function ф(t) of random variable X is defined for all values of t by et*p(x), if X is discrete e f (x)dx, if X is continus (a) Find the moment generating function of a Binomial random variable X with parameters n (the total number of trials) and p (the probability of success). (b) If X and Y are independent Binomial random variables with parameters (n1 p) and (n2, p), respectively, then what is the distribution of X...
Random variable X has MGF(moment generating function) gX(t) = , t < 1. Then for random variable Y = aX, some constant a > 0, what is the MGF for Y ? What is the mean and variance for Y ?
problems binomial random, veriable has the moment generating function, y(t)=E eux 1. A nd+ 1-p)n. Show that EIX|-np and Var(X) np(1-p) using that EIX)-v(0) nd E.X2 =ψ (0). 2. Lex X be uniformly distributed over (a b). Show that ElXI 쌓 and Var(X) = (b and second moments of this random variable where the pdf of X is (x)N of a continuous randonn variable is defined as E[X"-广.nf(z)dz. )a using the first Note that the nth moment 3. Show that...
Problems binomial random variable has the moment generating function ψ(t)-E( ur,+1-P)". Show, that EIX) np and Var(X)-np(1-P) using that EXI-v(0) and Elr_ 2. Lex X be uniformly distributed over (a b). Show that EX]- and Varm-ftT using the first and second moments of this random variable where the pdf of X is () Note that the nth i of a continuous random variable is defined as E (X%二z"f(z)dz. (z-p?expl- ]dr. ơ, Hint./ udv-w-frdu and r.e-//agu-VE. 3. Show that 4 The...
10. The moment generating function of the random variable X is given by My(t) = exp{2e* – 2} and that of Y by My(t) = fet +. Assuming that X and Y are independent, find (a) P{X + Y = 2). (b) P{XY = 0}. (c) E(XY).