function f(x for 0. (a) Find the mean and variance of X. b) Find the 3-rd...
Given f(x) = ( c(x + 1) if 1 < x < 3 0 else as a probability function for a continuous random variable; find a. c. b. The moment generating function MX(t). c. Use MX(t) to find the variance and the standard deviation of X.
function, s sin(x) if 0 < x <A otherwise Find the mean and variance of X. Find the mean and variance of the random variable X2 with the fol lowing distributions: - (i) X ~ N(u,0) - (ii) X ~ P(X) - (iii) X ~ Expo(1) "roblem 7 vandam variables,
10. If the moment-generating function of X is find the mean. variance. and omf of X.
Find the mean and variance of the random variable X with probability function or density f(x) f(x) = k(1 – x2) if –1 3x = 1 and 0 otherwise
Find mean and variance of a random variable whose probability density function is given by f(x) = C(x + 1) when -1<= x <=1 otherwise f(x) = 0 Find C values also.
Question 4: Find the variance of the exponential function using the moment generating function. f(x; 1) = {xe-x x>0 10 otherwise
(c) Find the variance of Y. 3. A random variable Y has the density function f(y) = Ky exp(-y/4), for osy<0. Then, [3+3+4=10 points) (a) Find the constant K. (b) Find the variance of Y. (C) Evaluate P(x > ).
Find the mean and variance of the random variable X with probability function or density f(x). 3. Uniform distribution on[0,2pi]. 4. Y= square root 3(X-u) /pi with X as in problem 3.
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.