f(x₁,x₂) = {Wx1x2, (Wx₁x₂, 0≤x₁ ≤ 1, 0 ≤ x₂ ≤ 1 elsewhere Find: i) the value of w that makes f(x₁, x₂) a probability density function.
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![f(x₁, x₂) = {Wx1x2,
(WX₁ X₂, 0≤x₁ ≤ 1,
0 ≤ x₂ ≤ 1
elsewhere
Find:
i) the value of w that makes f(x₁, x₂) a probability density function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3cf10f0-773a-49c2-8779-c91057a5176e%2F93918959-ea95-4756-b9ed-7b33d0a60ee7%2Fl9thl9_processed.jpeg&w=3840&q=75)
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- Let f(x) = Ce-x/1+e-2x for all x in (-infinity, infinity). If f is a probability density function for a random variable X on (-infinity, infinity), answer the following: (a) Find the value of constant C. (b) Evaluate the probability P(X<-4). Correct to four decimal places.5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = I > 0 (x+0)a+1³ is a probability density function. What can you say about the mean of a random variable that has fo,a as a pdf?The joint probability density function of X and Y is defined as f(r, y) = (1+2?)(1+y²) What is the probability that (X, Y) falls inside the square with vertices (0,0), (1,0), (1,1), and (0,1)? 16 O 1/2 O None of these. O 1/16
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