Let X be a r.v. with probability density function f(x)-e(4-x2), -2 < otherwise (a) What is...
2. Suppose a r.v. X has the density function 2 x, for 0<x<1 f(x) = 10, otherwise Observe X independently for three times, let y denote the number of an event {X<0.5) occurring in three times. (1) What is the probability of the event {X<0.5}? (2) What is the probability distribution of Y ? Write out its probability mass function
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval 0<x<2 (a) What is the support of X? (b) Letting S be the support of X, pick two numbers a, b e S and compute Pa<x<b). Draw a graph that shows an area under the curve y = f() that is equal to this probability. (c) What is Fx (2)? Draw a good graph of y=Fx (I). (d) What is EX? (e) What is...
2. Let X have probability density function JX2) = 1/2 0<x< 1 3 < x < 4 otherwise Find the cumulative distribution function of X.
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk. (5pts) Find 2. Е (X), (5pts) 3. the mode of X, (5pts) 4. the cumulative distribution function F(X) for all x. (5pts) 5. Evaluate P(X < 2.5). (5pts) 6. Deduce the value of the median and comment on the shape of the distribution (10pts)
Let X be a random variable with probability density function 2 (r > 1 0 otherwise. (a) Compute F)-P(X ) (the cumulative distribution function) for 1. Note that F(x) 0 for 1 (b) Let u-F(z). Invert F(-) to obtain 2 marks [1 mark 3 marks) F-1 (u), (z as a function of Your function should have:- Input: n - Number of samples to be generated. . Output: x - (xi, x2,, n) A vector x of n values from the...
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
4. [10 pts] Let X be a random variable with probability density function if 1 < a < 2, 2 f(a)a 0 otherwise. Find E(log X). Note: Throughout this course, log = loge.
Practice Exam Questions 2 Let X be a r.v. with density function x 2 1 a. Determine the distribution function of X, i.e. F(x). Find E(X) and V(X) b. Find the MLE estimator of θ constructed from a sample Xi,Xn c. Is the estimator find in (b) biased? Practice Exam Questions 2 Let X be a r.v. with density function x 2 1 a. Determine the distribution function of X, i.e. F(x). Find E(X) and V(X) b. Find the MLE...
4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0 < x, y < 4 and y> 4-1, otherwise. (a) Set up but do not compute an integral to find E(XY). (b) Let fx() be the marginal probability density function of X. Set up but do not compute an integral to find fx(x) when I <r54. (c) Set up but do not compute an integral to find P(Y > X).