A random variable X has the exponential distribution f(x) = hehx₂ x > 0 1. Show that the moment-generating function for t < λ f X is MX (1) = (1 - 1) . Find the mean and variance of X.

Q: Suppose you are given the moment generating function M(t) =- for t< In 3 4-3e Find the mean and…

A: The first derivative of moment generating function is, The mean of the distribution will be: Thus,…

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Q: 3. Suppose that X is a continuous random variable with pdf 32², 0<x< 1 0, otherwise Let Y= 2X + 3.…

A: f(x)=3x2; 0&lt;x&lt;1

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Q: Let X b(16, find E(4-3x) and distribution function.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: Suppose that f (x) = 0.125x for 0 < x < 4 %3D Determine the mean and the variance of X.

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Q: 68. Let X be a continuous random variable with pdf (a) Find the pdf for Y = √X. (b) Find the pdf for…

A: Pdf of X is fx(x)=3x2 ,0,&lt;x&lt;1

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A: It is an important part of statistics. It is widely used.

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Q: (1) Let X b(16, find E(4-3x) and distribution function.

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Q: Suppose X is a random variable with the cdf Fx(x) = 1-(1 + x²) x>0, C70, X>0 Derive the pdf of the…

A: Suppose X be the random variable with the cdf  FXx=1-1+xc-γ  ; x&gt;0, c&gt;0, γ&gt;0

Q: Find the mean and variance of

A: Given that fx=ke-2x,x&gt;0 The value of k is calculated below: ∫0∞f(x)dx=1∫0∞ke-2xdx=1ke-2x-20∞=1…

Q: Question is attached.

A: Given thatThe moment generating function of a random variable isTo find mean and variance:

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A: From the provided information, Mean (λ) = 2 X~exp(2)

Q: 1. Let X be an RV with PDF - f(x) = {1 = |x| a. Find the mean of g(x) = 5x² - 1. b. Find the…

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Q: If 1. If for >0 the energy of a pdf is E(x)=r, find the variance. (A) 1 (B) 2 (C) 1/2 (D) Undefined…

A: Step 1:Find the variance, The energy of a pdf is E(x) =x and x&gt; 0.Step 2:The variance is…

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Q: (22) Let X = b(6, find E(5+6x) and distribution function.

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Q: X is a continuous random variable and the pdf of X is x > 1 f(x) : xs1 Determine the value of k for…

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Q: 1. Let X have the pdf f (x) = B-l exp{-x/ß}, 0< x<o. Find the moment generating function, the mean,…

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Q: The moment generating function can be used to find the mean and variance of the normal distribution.…

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