A random variable X has a Pareto distribution if and only if its probability density is for a > 1 f(x) = elsewhere where a > 0. Find E(X) when a > 1. Find Var(X) when a > 2.

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Q: A continuous random variable X has the probability density function 2 -(9 – x) if 0 < x < 9 81 f(x)…

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Q: The lifetime in hours of a certain component of a machine has the continuous probability density…

A: Given that, The lifetime in hours of a certain component of a machine has the continuous probability…

Q: If the probability density function of random variable X is given by: {k(x - 1)(2 – x), 0, 1< xs 2;…

A: Given: f(x)=k(x-1)(2-x),         1≤x≤20,                                otherwise

Q: The probability density function of random variable X is given as: f(x) = {4 – Bx if 0 < x < 1…

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Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A: The probability density function of X is obtained below: f(x)=0.5e-0.5x;x≥0 where x is a random…

Q: A random variable X has the probability density function f(x) = e* on it support [0,z]. What is its…

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Q: The lifetime in hours of a certain component of a machine has the continuous probability density…

A: Given the continuous probability density function of the lifetime in hours of a certain component of…

Q: If a random variable X has the probability density function Sxe-* ,x > 0 ,otherwise' f(x) = Then…

A: Given,   fx = xe-x      ; x&gt;00             ; otherwise

Q: True or False The Poisson probability density P(x), when evaluated at x equal to its mean value, is…

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Q: with

A: Given: Computing CDF F(x) for X

Q: The probability density function of the random variable X is as in the picture with λ> 0. Find the…

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Q: The score of a student on a certain exam is going to be a number between 0 and 1. Think of it as the…

A: The probability density function is given as  f(x) = 4x0≤x≤124-4x12&lt;x≤10otherwise The cummulative…

Q: Determine the conditional probability distribution of Y given that X =1. Where the joint probability…

A: First we have to calculate the marginal density of X f(x).

Q: If X has an exponential distribution with parameter 0, use the distribution function techniques to…

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Q: A random variable has the following probability density function 1 -1--X <1 2

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Q: A filling station recieves its supply of gasoline once a week. Its weekly volume of sales in…

A: As given in the question that the weekly volume of sales is a random variable, Let this say X as…

Q: Let the continuous random variable X denote the current measured in a thin copper wire in…

A: Here X denotes current measured in copper wire in milliamperes. X ranges from 0 to 1/0.14. and  f(x)…

Q: Let the continuous random variable X denote the current measured in a thin copper wire in…

A: Answer - Let the continuous random variable X.  Assume that the range of X is [4.9, 5.1] mA,…

Q: The probability density function for a continuous random variable X has the form, Find the…

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

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Q: A continuous random variable has the probability density function f(x) = 1/8 for 0 ≤ x ≤ 8. What is…

A: Expected value of a continuous random variable:Continuous random variable:If the variable X takes…

Q: Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b)…

A: In particular, the cdf and pdf of X is, Since, ex is an increasing function of x and Rx = [0, 1],…

Q: A random variable X has a distribution function given by: (0, F(x)= {k(x-1)*, 13 1. Determine the…

A: Probability is the chances of occurrence of an event. The probability density function f(x) gives…

Q: A continuous random variable X has the probability density function if 0 < x < 8 { (8 – x) 32 f(x) =…

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Q: 3. If a random variable has the probability density for x>0 2e-2* f(x) = for x <0 Find the…

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Q: a) A random variable X has an exponential distribution with probability density function given by…

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Q: A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0<=x<=1, =0…

A: The given function is: f(x)=5-5x, 0≤x≤1

Q: 5. If the probability density function of a continuous random variable X is (cz" 0<x<1 f(r) =…

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Q: The(probability density function of a random variable, x is (x) = -(4 – x²) for 0< x < 2 4 = 0 %3D…

A: Introduction :

Q: Let X be a random variable with density x², 1<x<2 f(x)=• 0, otherwise Find F(x), the distribution…

A: To find the distribution function we have to integrate f(x).When x&lt;1 then…

Q: If the probability density of a random variable is given by JK (1 X2), 0< X < 1 0 < X< 1 fx (x) =…

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Q: The score of a student on a certain exam is going to be a number between 0 and 1. Think of it as the…

A: given that  the score of a student on a certain exam is represent by a number between 0 and 1…

Q: A continuous random variable X has the following probability density function: Jar² if-1≤x≤1 f(x) =…

A: Let x be a random continuous random variable such that (1) f(x) ≥0   for ∀ x (2) Sum of p.d.f. is 1…

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

A: Mean is a measure of central tendency and variance is a measure of dispersion. Mean is the…

Q: 11. If X has an exponential distribution with parameter 0, use the distribution function techniques…

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Q: A random variable has a probability density function .f(x)=cx(6-x)2 0<=x<=6 and 0 otherwise .…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 10. The probability density function for a continuous random variable X has the form, find the value…

A: For the given pdf Find c= ?

Q: If the probability density function of the random variable X is given by 0<x<1 f(x)={x otherwise

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Q: The probability density function of the continuous random variable X defined in the set of…

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Q: the distribution function of a random varlable X be if x 1 (a) Find the probability density…

A: (a) f(x) = ddx Fx(x)            =  123 x2+2 x ; if 0≤x≤1                            0 , otherwise…

Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A: Given, f(x) = 0.5e-0.5x : x≥0 where x is a random variable follows exponential distribution with…

Q: A continuous random variable has probability density function given by K(2x-3);1&lt;x2 Find k if…

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Q: The probability density function of a random variable is kx3 f(x) = if 0 <x< 2 V25 – x2 = 0…

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Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

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Q: x, ,x > 0 f(x; A) = {a otherwise

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Q: suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then…

A: In question, Given X has an exponential distribution with probability density function f(x) =2e^-2x,…

Q: Let X be a random variable with range [0 , 1] and probability density function (pdf) is given as:…

A: Let X be a random variable with range [0,1]and probability density function (pdf) is given as:…

Q: A continuous variable X has a probability density function given by p(x)=Ax^2 for 0≤x≤4, and p(x)=0…

A: Given that, A continuous variable X has a probability density function given by p(x)=Ax^2 for 0≤x≤4,…

Q: The probability density function of a continuous random variable is: 4 (1+x) if -1 < x < 0 x < 0) 5…

A: From the given information, fx=451+x, if -1&lt;x&lt;04153-2x, if 0≤x&lt;32   For -1&lt;x&lt;0,…