3. The density function of X is given by f(2) = {"* + bx? 0sxs 1 otherwise If E[X] = ; find a and b.

Q: The density function of X is given by f(x) = 1- x/2, for 0 < x < 2. Find E(5X?). Find Var(X).

A: Given,f(x)=1-x2     ;  0&lt;x&lt;20             ;  otherwise

Q: 1. The density function of X is given by f(x)=², 1≤1≤b. == If median is e³, find a and b.

A:

Q: 3. Suppose that X is a random variable with density function fx(x) and ImX = and suppose that Y =…

A: # Given pdf of random variable x is f(x) in :  0&lt;x&lt;1   Let y=e^x then to find pdf of y ?

Q: 16. Let a thin rod of length a have density distribution function p(x) = 10e-0.1, where x is…

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Q: Find the density function of Y.

A:

Q: 7.Find the value of k if f (x, y) = k(1- x)(1- y) for0 < x, y < 1 is to be joint density function.

A: We have given that f(x,y) = k(1 - x)(1 - y) , for 0 &lt; x , y &lt;1

Q: find Zrr and Zss for function Z(r,s)=ln(2r+3s)

A: Given that  find Zrr and Zss for function Z(r,s)=ln(2r+3s)find Zrr and Zss for function…

Q: Suppose fz(z) is a function given by So23 – 2) if -<<0 fz(2) = otherwise for a fixed constant c. Can…

A:

Q: Verify that the integral of the beta density from −qto q equals 1 for(a) α = 2 and β = 4;(b) α = 3…

A: The Beta density function is given by: We need to prove:

Q: A continuous random variable X that can assume values between x = 3 and x = 6 has a density function…

A: A continuous random variable X that can assume values between  has a density function given byFor…

Q: 4. The function f(x) = x cos(4x) is proportional to a probability density function on the interval…

A: The mean of a probability distribution function is EX=∫-∞∞x.fx

Q: . Let f (x) = cx 3 and S X = [0, 2] (X is continuous and c is a constant). a. What value of c will…

A: The value of c that makes probability density function valid is obtained below: From the given…

Q: 2. k) Show that fe2) = function is analytic %3D t'+s for Rez 70.

A: Calculate the limit: lim∆z→0fz+∆z-fz∆z=lim∆z→0∫0∞e-tz+∆zt2+1dt-∫0∞e-tzt2+1dt∆z…

Q: Let X, Y have range [0,3] and a marginal density functions, fx(x) = kx² an (a) Find k and the cdf of…

A: Solution: a. From the given information, the density function of x is The value of k can be…

Q: -5x Integrate x² e

A: We have to find

Q: Suppose you choose a real number X from the interval [2, 10] with a density function f(

A: Given that the density function for X is, fx=148x, 2≤x≤10

Q: Is the function defined as follows a density function? fx (x) = 0 for x < 2 (3 + 2x) 18 for 2 <x< 4…

A:

Q: Which of the following equations describes the relationship between the density function fy(y) for Y…

A:

Q: 7.Find the value of k if f (x, y) = k(1- x)(1- y) for0 < x, y < 1 is to be joint density function.

A:

Q: If f(1) = 4, f'(1) = 2 and g(x) = lInf(e*), then g'(0) is : %3D %3D %3D А. О в. O C. 2 С.2 D. 1 18…

A: Given: if f1=4, f'1=2 and gx=lnfex To Find: g'0 Concept: (i). Chain Rule for…

Q: (2x + 3y) if 0< x< 1 and 0< y) = otherwise

A:

Q: 1. Consider the two functions f(x) = C(2x - x³), g(x) = C(2x - x²), 0<x<2. (1) Could f be a…

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Q: 5. Given the density function of X as fx (x) = e iu (x), and T (X) = XI, then f, (y) is O eu (y)

A:

Q: fx(x) = (2) c² (0.95)³-²1{1,2,3,4,5) (2) a. с fx(x) = 2x +4¹(0-2)(x) b.

A: Solution