A random variable X has a Pareto distribution if andonly if its probability density is given by f(x) =⎧⎪⎨⎪⎩αxα+1 for x > 10 elsewhere where α > 0. Show that μ r exists only if r < α.

Q: Let X1,.X, be a random sample from a uniform (0,0) distribution and let Y = max(X1,..., the coverage…

A: We have a sample X1, X2,....,Xn from uniform distribution.  We know that, Y = max(X1, X2,....,Xn) =…

Q: If the random variable Y denotes an individual's income, Pareto's law claims that P(Υ y) = k where k…

A: given that  y is a random variable denotes an individual's income  k is the entire population's…

Q: Assume a continuous random variable X has a continuous uniform distribution between 35 and 48. Find…

A: given data  x is uniform distribution between 35 and 48 P(38&lt;x&lt;50) = ?

Q: Let X be a discrete random variable having the Poisson distribution with parameter u. we know that…

A: Let X be a discrete random variable having a Poisson distribution with parameter .We know that .

Q: Let X be a continuous random variable with a pdf f(x) = { kx5     0≤x≤1,             0…

A:

Q: Let X be a continuous random variable. Prove Var(X) > 0.

A: Solution:- Given that let X be a continuous random and prove that Var(X) &gt; 0.

Q: Let X be a discrete random variable having the Poisson distribution with parameter μ. we know that…

A: Let X be a discrete random variable having a Poisson distribution with parameter μ.We know that…

Q: Suppose the probability density function for a random variable X is given by S 24x- -4 if x > 2 f(x)…

A:

Q: Suppose that the random variable X satisfies P(X=a) = p and P(X=b) = 1-p, where a<b. Verify that…

A:

Q: Among all distribution laws of a continuous random variable X with the same known variation D, find…

A:

Q: Suppose x is a random variable best described by a uniform probability that ranges from 1 to 5.…

A: Answer:- Given, x is a random variable best described by a uniform probability that ranges from 1 to…

Q: A small petrol station is supplied with petrol once a week. Assume that its volume X of potential…

A:

Q: d) If probability density functions of a random variable x is f(x) = {X² for-1≤x≤1 for any other…

A: f(x)=x2 ; -1≤x≤1

Q: Show that if X is a random variable with continuous cumulative distribution function F(x), then…

A:

Q: Suppose that X has a continuous distribution with probability density function fx(x) = 2 * x on the…

A: Solution

Q: f (x) { kx, -1 < r < 1 0, kx², -1 <x < 1 = elsewhere

A: Answer - Given X has a probability density function               f(x)   = k x2                -1 ≤…

Q: Suppose that the discrete random variable X has cumulative distribution function given by if x < 1…

A:

Q: What is the probability that Q takes on a value between ½ and 1? What is E(Q)?

A: Let X be the random variable with pdf,

Q: Suppose that the random variable X has the continuous uniform distribution on the interval [0,1]. A…

A: It is given that X~U(0, 1).

Q: (a) Are X and Y statistically independent

A:

Q: If a random variable has the probability density f(x)= [2e-2x for x>0 for x≤0 0 find the…

A:

Q: Suppose that X is a continuous random variable with the following probability distribution: (refer…

A: Given that  Probability density functions of X is  f(x)=(x/18)  , 0&lt;x&lt;6

Q: 3. Let X be a random variable that is uniformly distributed on the interval (a, b). Find its moment…

A: Moment Generating Function for a random variable X is given by,  E(etX) = ∫-∞∞etxf(x) dx where f(x)…

Q: Let X be a Poisson random variable with parameter λ. Show that the probability that X is even is…

A: Given that, X be a Poisson random variable with parameterλ. We need to show that the probability…

Q: 7. Find the expected value of the random variable Y whose probability density is given by f(y) = 0…

A: Given that: Probability density function of Y: fy=18y+1      for 2&lt;y&lt;40…

Q: Let X be a random variable with probability density function   What is the probability P (X> 2)

A: Here we have give cumulative distribution function for F(x) = 1 - e^-2x

Q: A continuous random variable X has the distribution function F(x) = 0 if x 3 The value of k is

A: Given:  X has distribution function as : F(X) = 0 if X&lt;1 = k(x-1)^4 if 1&lt;X&lt;3 = 1 if X &gt;3…

Q: Suppose X₁,..., Xn are independent exp(X) random variables, where is the rate parameter. Find UMVUE…

A: Let X1, ......Xn are the independent exp(λ) random variables,where λ is the rate parameter.X¯ is a…

Q: (a) P(2 < Xs 5), (b) P(3 < X s 7), and (c) P(X 2 6). *

A:

Q: Suppose x is a normally distributed for continuous random variable with 4-10 and 6. Find value of xo…

A: First converting the variable into standard normal using z =(x-u)/σ where u is mean and σ is…

Q: Suppose that random variable X is uniformly distributed over the interval (0,1). Assume that the…

A: X follows U(0,1) Y|X follows B(n, x)   E(X) = ½ E(Y|X) =nx

Q: Assume that you have a sample 41-42»^ 100 from Weibull distribution .... = 120 -1 fr(x) = 2· exp(-x²…

A:

Q: Suppose that X1,.…,X, is a random sample from the Gamma distribution with density f(x; a, B) = r(a)…

A:

Q: Show that the Cauchy probability distribution does not have the first moment that is, E(X) does not…

A: The objective is to show the first moment does not exist for cauchy distribution

Q: Consider the following probability density distribution of random variable X. if 0<x < 6 f(x) = }kx…

A: Given function is f(x)={k            if 0&lt;x&lt;6kx+3k   if 6&lt;x&lt;100                otherwise

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.