The distribution function of a random variable X is given by F(x) ={ 0, for x <−1, (x+1)/2,−1≤x <1 ,1, x≥1.
Find
(a)P(−12< X <12);
The distribution function of a random variable X is given by F(x) ={ 0, for x...
The distribution function of a random variable X is given by F(x) ={ 0, for x <−1, (x+1)/2,−1≤x <1 ,1, x≥1. Find (a)P(−12< X <12); (b)P(1< X <2).
9. The distribution function of a random variable X is given by 0, for r<-1, F(x) = { 271 -1<x<1, 1, 2 > 1. Find (a) P(Z < X < }); (b) P(1<x< 2).
The distribution function of a random variable X is given by 0 Fw={ F(2) = 1+2 <-1 -1<r<1 => 1 "iszai (a) (5 points) Find the p.d.f(f(x)) of X (b) (5 points) Find P(0.3 < X <0.5)
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)
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)
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (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 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 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?
The cumulative distribution function for a continuous random variable X is given by 0, S 0 F(x) = 1, r 21. (a) Find the density fx for X. (b) Find the mean ? and variance ?2 for 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)