Let X be a continuous random variable with density f (x) = 24x-4 for æ > 2. Then Var (X) is equal to

Q: The number X is chosen at random between 0 and 1. determine the density functions of the random…

A: Given information: The number X is chosen at random between 0 and 1.  fx=11-0,…

Q: A system consisting of one original unit plus a spare can function for a random amount of time X. If…

A: Given,For the probability density function, total probability is equal to 1,i.e., 4C=1

Q: ariables X and Y are JO two stafistically independent random fx(x) = fu(x – 1)e-x-1)/2 fr(y) = u(y-…

A: Solution

Q: let fx(x,y)= 1/x, 0<y<x<1 derive distribution of y and compute e(y) and var(y)

A: Given fx,y=1x ; 0&lt;y&lt;x&lt;1

Q: A system consisting of one original unit plus a spare can function for a random amount of time X. If…

A: If a system consists of  original unit plus a spare, then it can function for a random amount of…

Q: If X has the uniform density with the parameters α = 0and β = 1, use the distribution function…

A:

Q: total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one…

A: Let the random variable x has the density function     f(x) = x     ,  0&lt;x&lt;12-x   ,  1≤x&lt;20…

Q: Suppose that the random variable X has density fx (x) = 4x³ for 0 X).

A: Independence of pdf applied.

Q: Let X be a continuous random variable with a uniform distribution in the interval [0, 1], i.e., X ∼…

A: The transformation of a random variable involves creating a new random variable through a function…

Q: If the continuous random variable X has the probability density ( 62(1 - 2) for 0<z<1 elsewhere f(2)…

A:

Q: fx1,x₂(x1, x₂) = 0, otherwise. What is the joint probability density function fy₁,Y₂ of Y₁ = X₁/X2…

A:

Q: For the random variable X with the density function f(x) = {2/ compute Var(X): ☐ and sd(X): 2/x2 for…

A: Step 1: The probability density function of the random variable X is,  Step 2: The variance of X is,…

Q: Consider the random variable X with the uniformdensity having α = 1 and β = 3.(a) Use the result of…

A:

Q: Let X = (X,,X,,..., X„) be a random sample with size n taken from population has probability density…

A: We want to prove that U=min(X) is the sufficient for θ.

Q: The random variable X has probability density function f where f(x)=\ ( kx(x + 1) (2-x ), 0 <= chi…

A: The probability density function is given as,