The following ψ are m.gf of some random variable X. Find EN] and Var(X) in each...
Find Var(2X-Y)
Two random variables X and Y are i.i.d. and their common p.d.f. is given by f )- c(1+r) if 0 <r < 1. otherwise. f(3) = 10
3.81 The random variable X has moment generating function M (1) = 0.2e41 + 0.7e7t + 0.1 e9t -oo < t <00, Find P(X = 7).
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).
3-) Let ocr<1 o w UUUUU is probability destiny function of X random variable. a- ) Find PlOCXCI) b.) Find Pix > 15) UUUUUU ca) Find € (x) and Var(x) d-) Find the distribution function
(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.
Suppose X is a continuous random variable having pdf (1+x, -1 < x < 0, f(x) = { 1 – x, 0 < x <1, lo, otherwise (a) Find E(X2). (b) Find Var(X2).
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
Let X be an exponential random variable such that P(X < 27) = P(X > 27). Calculate E[X|X > 23].
Suppose that the cdf of random variable X is Skex-3, X <4 11, X >4 Find k. (2 Points) Find the expected value of X. (2 Points)
The random variable X has the probability density function (x)a +br20 otherwise If E(X) 0.6, find (a) P(X <름) (b) Var(x)