8. Suppose the cumulative distribution function is F(x) {1-12 x21j. (3pts) Find the median, i.e. find...
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].
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
Let X be a continuous random variable with cumulative
distribution function F(x) = 1 − X−α x ≥ 1
where α > 0. Find the mean, variance and the rth moment of
X.
Question 1: Let X be a continuous random variable with cumulative distribution function where a >0. Find the mean, variance and the rth moment of X
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?
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
8. Let f(x) = c / x. For x >1. Find c and the median.
5. (20 pts) Determine the expectation, variance, standard deviation, cumulative distribution function (c.d.f.), and median for each of the following: (a) f(x)-름 (z-1.5) for 2 rS 5 (b) f(x) = Lp (c) f(x) = d for 40 < x < 100 (d) f(x)- e-z/2 for x 20 1.25 for 1<x<5
X is a discrete random variable with cumulative distribution function F(x) as shown in the table below. What is P1[.X<2]? fr F(x) 1/8 30-as 0 100 - 0 m 0 oon 100 0 0 O E. cannot be determined
Let X be a random variable with the following cumulative distribution function (CDF): y<0 (a) What's P(X < 2)? (b) What's P(X > 2)? c)What's P(0.5 X < 2.5)? (d) What's P(X 1)? (e) Let q be a number such that F(0.6. What's q?
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