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, X2, X3, X4 be a random sample from the distribution with PDF f(x) = e¯, x > 0. Calculate the…

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Q: A continuous random variable X has probability distribution function f(x) , where f(x) = k(1 − x2)…

A: The k value is calculated as follows:

Q: Suppose that Y₁, Y₂,..., Yn is a random sample from a population with probability density function…

A: Find the likelihood function and maximize it.

Q: Suppose X is a random variable taking values in the interval [0,2] with probability density function…

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Q: 2. Suppose that the random variable X possess a uniform distribution on the interval (0, 1). Let…

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Q: Let X be a continuous random variable with PDF 2x 0 < x < 1 fx(x) = {0 otherwise Find the expected…

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Q: If X has an F distribution with ν1 and ν2 degrees offreedom, show that Y = 1Xhas an F distribution…

A: Note: Thank you for the question. Since the information is not clear to us, we have considered,…

Q: If the probability density of X is given by f(x) =2x−3 for x &gt; 10 elsewherecheck whether its mean…

A: Solution: From the given information, the probability density function of X is

Q: Suppose that the random variable W has a beta distribution with probability density function f (w)…

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Q: Find the value of c such that an interval from x to cx is a (1- a)100% confidence interval for the…

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Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: We want find  Mean= E(x) , variance = var(x)

Q: f (x) Suppose a continuous random variable X has the probability density K (1-x²) for 0 < x < 1, and…

A: It is give that  a continuous random  variable X has the probability  density function f(×) =…

Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: What is the variance of X

A: here given continuous probability density function  c(1- x2)           -1 ≤x ≤ 10…

Q: The random variable X has probability density function 1 < x < 2 f(x) = otherwise. Calculate Var(4X…

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Q: The random variable x follows a uniform probability distribution in the interval (0,1); the…

A: We know that  The pdf of Uniform distribution is  f(x) = { 1/(b-a) ,   a&lt;x&lt;b                0.…

Q: If Y is a standard Cauchy random variable, show that Y and are identically distributed. Y

A: Solution

Q: For the continuous probability functionf(x) = Kx when x20 find

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Q: (Y-1)². Use one decimal place accuracy.

A: Given that  Y ~ Uniform (1 , 11)

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: Suppose that the continuous random variable X has cumulative distribution function given by F(x)=…

A: Given that, X is a continuous random variable. X has a cumulative distribution function Fx. Fx is…

Q: find the value K and F(x).

A:

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: A random variable X has a Pareto distribution if and only if its probability density is for a > 1…

A:

Q: Suppose that the random variable X has the probability density function c(1– x?) for - 1< x <1 f(x)…

A: Answer - The random variable X has  the probability density function                f(X) = c(1-x2)…

Q: Assume that X donotos the continuous random varlable with probability distribution of y & (A) and…

A: Basic probability

Q: A random variable X follows a uniform continuous distribution on the range [0, B]. Use mathematical…

A: Uniform distribution: A continuous random variable X is said to follow Uniform distribution if the…

Q: (4) Let X be a discrete random variable with domain D. Prove that Var(X) = E(X?) – E(X).

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Q: Let X,, X2,... ,X, be a random sample from a distribution with density function if x20 f(x; 0) =…

A: Answer is given using concept of density function.

Q: b) The probability density function of random variable X is given as: f(x) = {* |– Bx if 0 <x < 1…

A: Given that  We have to find value of A and B :

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.