2-2.3 A probability distribution function for a random variable has the form F,(x) = A(1-exp[-(x-1)) 1...
A probability distribution function for a random variable X has the form Fx(x) = A{1 - exp[-(x - 1)]}, 1<x< 10, -00<x<1 (a) For what value of A is this a valid probability distribution function? (b) Find the probability density function and sketch it. (c) Use the density function to find the probability that the random variable is in the range 2 < X <3. Check your answer using the distribution function. (d) Find the probability that the random variable...
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)
3,40 A random variable X has probability density function fx(x) = 1 0<x< 1. Find the probability density function of Y = 4x3 - 2.
7. A random process may be modeled as a random variable with the probability density function fx(x) fx(x) fx(x) x < 1/2 x 1 /2 = 2-4x = 4x-2 = 0 (a) Show that Jdfx(r)dr = 1 (b) Find the CDF, Fx() (c) Find the probability that X is between 1/3 and 2/3. (d) Find the expected value of X. (e) Find the mode of X (f) Find the median of X. (g) Find the variance of X and the...
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...
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.
X, be a random sample from a distribution with the probability density function f(x; θ) = (1/02).re-z/. 0 <エく00, 0 < θ < oo. Find the MLE θ
Problem 5. Suppose that the continuous random variable X has the distribution fx(x), -00 <oo, which is symmetric about the value r 0. Evaluate the integral: Fx (t)dt -k where Fx(t) is the CDF for X, and k is a non-negative real number. Hint: Use integration by parts
2. Determine whether the function f(x) is a valid probability distribution (PMF) for a random variable with the range 0,1,2,3,4 12 f(x) = 30 3. Suppose X is a random variable with probability distribution (PMF) given by f( and a range of 0,1, 2. Find the distribution function (CDF) for X 6
-l0 1- e-2x x MO 2) The distribution function for a random variable X is f(x) x <0 Find a) the density function 2 b) the probability that X 4 c) the probability that -3 <x 6inotion