2. Calculate the expected value of the following continuous density function: 2 (x+2) 5 oroye f(x)...
Let X be a continuous RV with the following density function: f X ( x ) = { 2(1 − x ) , 0 < x < 1 0 , elsewhere a. Determine the cumulative distribution function for X , F X . b. Compute P ( X ≤ 0 . 5). c. Compute the mean of X , μ X . d. Compute the median of X . e. Compute the variance ( σ 2 X ) and standard...
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continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
5. (Expected value) Let X be a continuous random variable with probability density function S2/a2 if 1 2, f(x) elsehwere. 0 Find the expected value E (In X). Hint: Integration by parts
onsider X is a continuous variable with the following density function f(x) = 2(x - 1) 1<x<2 otherwise (a) Compute expected value of the random variable X (b) Compute standard deviation of the random variable X (c) If g(x) = 4x + * 4X + 2, what is the expected value of g(x)? (d) What is the standard deviation of g(x)?
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
(a)The continuous random variable X is distributed with probability density function f defined by f(x) = (1/64)x * (16 - x^2) , for 0 < x < 4. . Find [V (2x+1)] . (b) -An urn contains 7 white balls and 3 black balls. Two balls are selected at random without replacement. What is the probability that: 1-The first ball is black and the second ball is white. 2-One ball is white and the other is black ( C)- Suppose...
please I need detailed explanation
The density function of a continuous random variable X is 4(9-2) 8 i 0 elsewhere Find: (a)the mean, mode and median of X. (b) the semi-interquartile range and the mean deviation of the distribution (c) the coefficient of skewness and kurtosis of the distribution.
1. Let X be a continuous random variable with the probability density function fx(x) = 0 35x57, zero elsewhere. Let Y be a Uniform (3, 7) random variable. Suppose that X and Y are independent. Find the probability distribution of W = X+Y.
6) If the probability density function of a continuous random variable X is f(x) =x/8 when 3<x < 5, f(x)=0 otherwise a) Find the expected value of this distribution. b) Find the variance of this distribution. c) Find the 25th percentile of this distribution.
Show that the function f(x)=1/(x^2+π^2 ) can be taken as a
probability density (distibution) function of a random variable X.
Find p(X>π). Find also the cumulative distribution function F(x)
of the random variable X. Find, finally, mean and standard
deviation of the random variable X
1 Show that the function f(x) = can be taken as a probability density (distibution) x²+x² function of a random variable X. Find p(x > 1). Find also the cumulative distribution function F(x) of the...