Let X be a continuous random variable with density function be-bx for a > 0 otherwise , f(x) = where b> 0. - find M(t) the moment generating function of X, then what is E(x) ?

Q: suppose that the probability density function of x is f(x)={3x^2, 0, 02/3)

A: 3. Given f(x)=3x2, 0<x<1 Consider, P(X<13)=∫0133x2dx               =3x3301/3…

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 random variable X has the probability density function 1 1 f(x) = n x2 + 1' then the probability…

A: Here we've to find, P(1/3<X2<1) We can write it, P(√1/3<X<1)

Q: fr(y) =(y-3)e Find the probability density of the sum W =X + Y.

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Q: 5) Given X with the probability density function: 4x, if 0<x< 1 0, otherwise fx(x) 6) = Determine…

A: Check the solution in the explanation.Explanation:Check the image below for a detailed solution.

Q: Random variables X and Y have density functions £x(x) == [u(x)-u(x-a)] a and fy(y) = bu(y)e-by where…

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Q: The lifetimes X and Y (in years) of two machine components have joint probability density (5 – x –…

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Q: Let x be a random variable defined by density function fx=3x^2 define less than equal to 1 and great…

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Q: a) A continuous random variable Y has density function 3-2y f(y)={3 e „y > 0 ,elsewhere Find the…

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Q: Suppose that the random variables Y1 and Y2 have joint probability density function f(yn.2) given by…

A: Given that f (y1 , y2 ) = 6y12 y2 , 0≤ y1 ≤ y2 ,    y1   + y2  ≤ 2

Q: 6. (18 points) The time X between customer arrivals at a bank branch has density function S(æ) = { S…

A: Given, The density function is, f(x)=kx2                              0≤x≤3

Q: technique to find the density function for the random variable Y. The density function should be…

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Q: (i) determine how to generate a random variate X. (ii) generate random variate X, uniformly…

A: For generating a random variate that follows a particular distribution, the inverse transform method…

Q: Question is attached.

A: (a)The value of c can be derived as follows:

Q: The density function of X random variable is given below: 1<1< 3, fz(z) = otherwise. Y random…

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Q: nd the probability density of the sum W = X + Y.

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Q: Let (X, Y) be bivariate random variables having joint probability density function as f(x) = {;x +y)…

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Q: Consider the following interesting probability mass function for a random variable X with A > 0 p(x)…

A: Probability Mass Function: A discrete function f(x) is said to be the probability mass function of…

Q: et the density function of a random variable Xt fx(x) = Ox®-1, 0sxs1 0<x<1 ompute the sufficient…

A: The pdf of random variable X is given: fX(x) = θ xθ-1,   0≤x≤1

Q: (a) Let Z = vX. Show that the density function of Z is given by %3| (-). fz(z) = 2a exp z > 0.

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Q: b) N(0,1), and W₁ = N(0,1), for i = 1,2,3,...,10, then: dx i) State, with parameter(s), the…

A: Given Zi~N(0,1) and Wi~N(0,1)  Result: t~F(a,b) Then  Mean=E(t)=b/(b-2) V(t)=2b2…

Q: 9 Let the probability density of the two-dimensional random variable (5, n) be (4e", x>0; f(x)=10.…

A: The probability density function for the two variables are : fξ(x)=4e-4x ,x&gt;0fη(y)=6e-6y ,y&gt;0…

Q: A random variable X has the density function f(x) = c/(x² + 1), where -<x < 0. (a) Find the value of…

A: a) The total probability is always 1. Using that we get:…

Q: Let Xa random variable with density function f (x) = e-® . 1(0,00) (2). Determine tha density…

A: # Given: random variable x follow exponential (1) distribution then to find pdf of y=x/(1+x)

Q: Is f(x) a legitimate probability mass function? 1- p)*-1p = p+(1 – p)p + (1 – p)°p +. 1 %3D x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x.  And the sum of all…

Q: The density function of X is given by f(x) = a + bæ, 0< x < 1. (1) If E(X) = , find a and b. (2)…

A: density function of X is given by;f(x)=1+bx,  0≤x≤1

Q: (x + ax², 0 < x < 1 diğer fx (x) = 0,

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Q: One recognizes the integrand of Equation (23) as a r(a, 6) density, hence M (t) = (;)"(1) = (24) |3|…

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Q: Find the cumulative distribution function (C.D.F) of a random variable Y, whose probability density…

A: The probabiilty density function of Y is,

Q: function is given by: ´ay§ fy) = {ya+1 (0, if y > yo elsewhere ii) Show whether or not that the…

A: Solution