X follow uniform distribution
min(x,4) = x when x < 4
= 4 x >= 4
=
b)
Please rate
A continuous random variable X has a density function f(x)= otherwise Calcate min(,4)f() anmi )dr
Let X be a continuous random variable with density function f(x) = ''9. O , otherwise. Find the mode of X
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
2. The random variable X has probability density function f given by f(x) 0 otherwise. (a) Is X continuous or discrete? Explain. (b) Calculate E(X). (c) Calculate Var(2X 9).
A continuous random variable X has the density 3 x for f(x) = 0 otherwise. What is the probability that X is greater than its 75th percentile?
Let X be a continuous random variable with probability density function fx()o otherwise Find the probability density function of YX2
Let X be a continuous random variable with probability density function fx()o otherwise Find the probability density function of YX2
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
Let X be a continuous random variable with density function 0, otherwise. alculate the value of p such that E(X-
A continuous random variable X has probability density function f(x) = a for −2 < x < 0 bx for 0 < x ≤ 1 0 otherwise where a and b are constants. It is known that E(X) = 0. (a) Determine a and b. (b) Find Var(X) (c) Find the median of X, i.e. a number m such that P(X ≤ m) = 1/2