3.1 Solve the below problem: Let Y, and Y2 have a joint density function given by 0 < y2 s y1 S 1 elsewhere. (3y1 %3D 3.1.1. The marginal density function for Y2 is f(y2) =(1- y?), 0 < y2 < 1. Find the marginal density function of Y,. (NB: Show all your calculations) 3.1.2. The conditional density of Y2 given Y, = y, is f(y2ly1) =. Find E (Y2|Y, = y1). 0 < y2 < y1 < 1.

Q: 9. Find the characteristic functions of the following density functions: (a) f(x) = ex for x € R,…

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Q: 2. Density with unknown a. Find a such that ax², 1<x < 5, f(x) = { 0, otherwise. density, pdf f(x)…

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Q: (ii) Calculate E[eX/³[Y = 1].

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Q: Q: Suppose fy (y) = 4y³, 0 < y < 1. Find P(0 < Y <;)

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Q: Consider the following joint density function: f(x,y) = ÷(x + 3y²), 0 < x < 1,0 < y < 2.…

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Q: Consider the density function f(x) = k√√x, 0<x<1, 0. elsewhere. (a) Evaluate k. (b) Find F(x) and…

A: The PDF is given asWant to calculate the distribution function F(x)?Know that the distribution…

Q: 2. Aprobability mass function is given as f(x) =- for x = 0,1,2,3,. Find P(1.5 < X < 4.2)

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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: 1.5 Solve the below problem: Let Y, and Y, have a joint density function given by fU1, 92) = (3y1 0<…

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A: Let random variables X1 and X2 be the proportions.The joint PDF of X1 and X2 is ,The question…

Q: 3.21. Write an expression for the autocorrelation function R,(t), where 5 y(t) = EY„Rect( ) and {…

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Q: (d) What is the median checkout duration ? [solve 0.5 = F()]. (e) Obtain the density function f(x).…

A: Since you have asked multiple questions, we will solve first three subparts for you. To get…

Q: I 2 Find Mass, Mx, My and and y of the Lamina bounded by y = -3.x +3, y= and x=0. and with the…

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Q: 2. (a) The following is a two-parameter gamma density function: f(x;a, B) = where a >0,B >0,x.…

A: The PDF for the two-parameter gamma distribution is : f(x;α,β)=βα.xα-1.e-βx(α-1)! (i)…

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Q: [8] 3. In a process of sintering(heating) two types of copper powder, the density function for Y1,…

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Q: Suppose X and Y have joint density given by, 1, 0<x < 1,0 <y<1 f(x, y) = 0, otherwise 1. Prove that…

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Q: N 15. The density for X, the number of holes that can be drilled per bit while drilling into…

A: Please refer below page.If you have any questions feel free to ask.Explanation:

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Q: 1. Let f(x, y) = where C is a constant. (x2 + 1)(y² + 1) ’ For which value of C is ƒ a joint density…

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Q: Find the CDF.

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Q: Question 8 The joint probability density of X and Y is f(x, y). Find the marginal density of X at…

A: Given: joint pdf of random variable x and y is f(x,y)=2xy  :0&lt;x&lt;1, 0&lt;y&lt;2 , y&lt;2x  then…

Q: Consider the transformation Y= 1/X, and the density function f(x) = 3*x² for 01 The density function…

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Q: Let fi(x) and f2(x) be two density functions on (-o, 0). Prove fi(x)log(2))dx < 0 $2(x).

A: Given See the handwritten solution

Q: Let Y₁, Y2,..., Yn be random sample whose density is given by fy(y) = aya-1 θα " 0≤ y ≤0 where now…

A: To find the sufficient statistics for , we can use the factorization theorem, which states that a…

Q: Q8. If f(x,y) = {o (24xy, 0 sx s 1 ,0 sysi x+ys1 is a joint density function of X and Y. Find the…

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Q: erved outcome X is 32 f(x) = }(x + 4)³ x20 otherwise Eulate P (x 2/xs). (CLO-1: PLO-1:C1) (4,4)

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Q: 2.1 Solve the below problem (show all calculations). Let Y, and Y, be random variables with joint…

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Q: Find Mass, Mx, My and a and y of the Lamina bounded by y = -9.x +3, y and z = 0. and with the…

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Q: The marginal density functions of X and Y are and £x(x) = [** £x,y(x,y) dy = @F(x,∞) əx fy(y) =…

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Q: P4. A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X…

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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.

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Q: Verify that the above is a valid density function. A batch is considered not sellable and then not…

A: It is given that Y : proportion or percentage of impurities in a batch.

Q: 3.21. Write an expression for the autocorrelation function R,(t), where 5 y(1) = E Y,Rect() and {…

A: Given, y(t)  = ∑n = 15 Yn Rect t - n52   andYn = 0.8, 1, 1, 1, 0.8