A continous random variable X has the density function. f(x) = {x,            0 < x ≤ 1,          {2 − x,     1 < x ≤ 2,           {0,           elsewhere. (a) Show that P(0 < X < 2) = 1 (b) Find P(X < 1.2)

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A: INTRODUCTION:  Let X and Y be two discrete random variables. Then the two random variables X and Y…

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Q: 1.) A random variable x has a density function given by: Sk(x + 1),0 1.5) c.) F (x)

A: I solved exactly first three subparts because of bartleby policy if you want more please uplode…

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Q: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0&lt;x&lt;3,0&lt;y&lt;3

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Q: Let X and Y has joint probability density function AX, Y) = 0<x<2, 0<y<2. 16 Find E( X Y ).

A: Solution: From the given information, the joint probability density function of X and Y is

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Q: The density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).

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A: f(x) = kx12e-x , x&gt;0∫f(x) dx  = ∫0∞kx12e-x dx = 1⇒k∫0∞x12e-x dx = 1⇒k∫0∞x32-1e-x dx=1⇒∫0∞x32-1e-x…

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Q: 4. A continuous random variable x that can assume value between x = 2 and x = 5 has a density…

A: Solution-: We have following density function    ; We find, (a) P(X&lt;4)=? (b) P(3&lt;X&lt;4)=?

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A: Note: According to Bartleby guidelines expert solve only one question and rest can be reposted.

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Q: 1. A random variable X has a density function f(x) = cx² CX 2<x<3 otherwise 1. P(1/2 <X <3/2)

A: We have to find the value of constant for valid pdf and also have to find the probability.

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