Suppose that an Random Variable X has a Cumulative Distribution Function that takes only two values. Show that X there exists c such that P (X = c) = 1.
Suppose that an Random Variable X has a Cumulative Distribution Function that takes only two values....
Exercise 3.37. Suppose random variable X has a cumulative distribution function F(x) = 1+r) 720 x < 0. (a) Find the probability density function of X. (b) Calculate P{2 < X <3}. (c) Calculate E[(1 + x){e-2X].
Problem 3. Suppose that the cumulative distribution function of a random variable X is given by (o if b < 0 | 1/3 ifo<b<1B 2/3 if isb<2 2.9 1 if2 Sb. 3.9 (a) Find P(X S 3/2). (b) Find E(X) and Var(X). 4.10
Suppose that X is a random variable whose cumulative distribution function (cdf) is given by: F(x) = Cx -x^2, 0<x<1 for some constant C a. What is the value of C? b. Find P(1/3 < X < 2/3) c. Find the median of X. d. What is the expected value of X?
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
Question 2 If the random variable X has the following cumulative distribution function, find the cumulative distribution function for Z vX. x < -1, x< 0, Fx(x) 1/3, 1,
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a Inz, a<<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function S(x) for X. (d) Find E(X)
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a F(x) = Inr, asi<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(x > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
Suppose the cumulative distribution function of the random variable X is 0, x-0.8 F(x)-0.25x + 0.2,-0.8 sx <3.2 1,3.2 sx Round your answers to 3 decimal places Determine the following ) P(X 1.8)-065 b) P(X >-1.5) = c) P(X -2) exact number, no tolerance
A random variable X has the cumulative distribution function F(x) = 1-e^(-1.54x), x ≥ 0 a. Compute P(X ≤ 0.69) b. Compute P(X > 0.64) c. Compute P(0.69 < X ≤ 2.61)