9. The distribution function of a random variable X is given by 0, for r<-1, F(x)...
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)
The cumulative distribution function of the random variable X is given by F(x) = 1-e-r' (z > 0). Evaluate a) P(X > 2) b) P(l < X < 3 c) P(-1 〈 X <-3). d) P(-1< X <3)
1 A continuous random variable has its cumulative distribution function of the form: 0 2<-1 F() = k(x+1) -1<x<0 1 2 > 0 Which of the following is the pdf for this distribution? 0 2-1 of() = {2.(2+1) -1 <o<0 2 > 0 0 x<-1 Of(0) = { 1.(2+1) -1 <<<0 0 2 > 0 1 <-1 of(x) = { $.1.(2+1) -1 <<<0 20 0 <-1 of(x) = { 2. (+1) -1<x<0 0 2 > 0 None of the above....
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).
(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)
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
(+3) The pdf f(x) of a random variable X is given by 0, ifx<0 Find the cumulative distribution function F(r
1. Given the piece-wise function, 3x if x < 0 f(x)=x+1 if 0 < x 52 :- 2)2 if x>2 Evaluate f (__); f(0); f (); f(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)
Show steps, thanks! 2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.