is a continuous random variable with the probability density function
(x) = { 4x 0 <= x <= 1/2
{ -4x + 4 1/2 <= x <= 1
What is the equation for the corresponding cumulative density function (cdf) C(x)?
[Hint: Recall that CDF is defined as C(x) = P(X<=x).]
is a continuous random variable with the probability density function (x) = { 4x 0 <=...
A probability density function f of a continuous random variable x satisfies all of the following conditions except a) b) c) For any a,b with , P() = d) The mean and variance of a probability density function f are both finite We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let A be a continuous random variable with probability density function Random variable D is given by ---------------------------------------------------------------------------------------------------------------- (a) What is the probability density function of D? specify the domain of D. Answer is - - (b) Find E(D) and Var(D). fa(a) = -a? 9 0<A<3 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let X be a continuous random variable defined on the interval [0, 4] with probability density function p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than some number a, assuming 0 < a <...
1. Let X be a discrete random variable with a cumulative distribution function: a. Use this cdf to fin the limiting distribution of the random variable when with , as n increases. Use the fact b. What kind of random variable is for large value of n? We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagep= We were unable to transcribe this imageWe were unable to transcribe this imageWe were...
The probability density function of a continuous random variable X is given as shown. I f(x) a) (7.5 pts) Find the value of the constant k as a fraction. b) (7.5 pts) Find the probability P(1sx53). c) (5 pts) Find the value of x such that P(Xsx)=0.5.
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)
Assume the continuous random variable X follows the uniform [0,1] distribution, and define another random variable We were unable to transcribe this imagea) Determine the CDF of Y. Hint: start by writing P(Y ), then show that P(Y y) = P(X s g(v)), where g(y) is a function that you need to determine. b) Determine the PDF of Y.
Continuous random variable X has pdf for , where is symmetric about x = 0. Evaluate where is the cumulative distribution function of X and k > 0. fr) We were unable to transcribe this imagefr) We were unable to transcribe this imageFr(r
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
Suppose that X is continuous random variable with 2. 1 € [0, 1] probability density function fx(2) = . Compute the 10 ¢ [0, 1]" following: (a) The expectation E[X]. (b) The variance Var[X]. (c) The cumulative distribution function Fx.