Suppose that Y has density function f (y) = $ ky(1 − y), 0 ≤ y ≤ 1, 0, elsewhere. a Find the value of k that makes f (y) a probability density function. b Find P(.4 ≤ Y ≤ 1). c Find P(.4 ≤ Y < 1).

Q: Let V = X+ Y and W = X/Y. Show that the joint density of V and W is given by 1 fv,w(v, w) = 27 /w(w…

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A: The answer to the above question is as follows : X~exp(2)f(x)=2e-2x…

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A: Given that the random variables and  have joint probability density function :

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A: Explanation of the answer is as follows

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Q: Let the random variable X have the density function f(x)= (kx,0 ≤ x ≤ √2/k lo, elswhere

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Q: Let X and Y has joint probability density function AX, Y) = *7 ,0<x<2, 0 <y<2. x y Find E( X + Y)

A: Given a joint probability density function of X and Y , we need to find E( X+Y)

Q: 10. Ifa continuous random variable has the density function fæ) = 0.003x? ,0 < x< 10 then P(X <…

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A: Note: According to Bartleby, expert can solve only one question and maximum 3 subpart of the first…

Q: Q6. Consider the probability density function fex) = {C A if x>1 Inx %3D X2 otherwise . Ca) Find C.…

A: Given function f(x)=clnxx2if x≥100therwise find c find Px≥3

Q: 9. Is the function defined by f(x)=0 = 1 18 =0 (2x+3) x4 a probability density function? Find the…

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Q: 10. If a continuous random variable has the density function fe) = 0.003x? ,0 <x< 10 then P(X <…

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Q: Give the two conditions that a probability density function for [a, b] must satisfy.

A: The probability density function f(x) lies in close interval a to b.

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Q: 20 Select the correct answer. For what constant k is RX) = ke *- 1 a probability density function on…

A: 20) The value of k is,

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Q: Let the random variable X have the density function = {kx₂,0; f(x) (kx,0 ≤ x ≤ √√2/k 0,elswhere

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A: Solution

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A: Given: The probability density function of random variable X is given as:…

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A: Given that

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Q: i. A valid probability density function satisfies 0 ≤ fx(x) ≤ 1

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Q: Suppose that X is a continuous random variable with density function f(x). If f(x)=k for -3 ≤ x ≤ 2…

A: For f(x) to be a density function, we need      (i) f(x) ≥ 0      (ii)  -∞∫∞ f(x)dx = 1

Q: A random variable X has the density function: f(x)= K.1/(1+x2), if− ∞ < x < ∞ . Determine K and the…

A: From the given information, PDF: fx=k1+x2,-∞&lt;x&lt;∞ Thus, a) Value of k can be computed as:

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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A: Given, The density function of X1 as: Conditional distribution of X2 given X1=x1 is:

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A: According to the answering guidelines, we can answer only three subparts of a question and the rest…