Find a constant C such that JC(4x – y + 3) if 0 < x < 2 and 0 < y< 3 p(x, y) = otherwise is a probability distribution and calculate P(X < 1; Y < 2).
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A: Given :
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Q: the probability
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Q: Suppose that Y is a continuous random variable. Show EY = yfr(y)dy.
A: Here, we have to prove EY=∫-∞∞yfydy.
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Q: b) For the triangular function c(10-x) 0<x<10 f(x)={° otherwise Find the value of c which makes the…
A: From the provided information,
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A: Here the given function is : We have to find the value of c .
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Q: P(-∞ < x≤ a₁₂) = P(a₁ ≤ x ≤ a₂) = P(a₂ ≤ x ≤ a3) = P(a3 ≤ x < ∞) = function p(x) a₁ = = 1 π(1 + x²)…
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A: The required probabilities are as follows:
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- If 2 > 0 and X is a continuous random variable with p. d.f. 22xe-dx ,x 2 0 ,otherwise f(x) = Then var(X) is:Assume that X is a random variable whose conditional distribution given the variable Y is poisson P (X | Y) = Po (Y). Suppose further that Y has a gamma distribution Y ∼ Gamma (1, 1). (a) Determine the value E (XY). (b) Determine the conditional distribution P (Y | X).Let X₁, X2, X3, be a random sample from a discrete distribution with probability function p(x) = for x = 0, for x = 1, otherwise. Determine the moment generating function M(t) of Y = X₁X₂X3- A. exp(t) B. (exp(t)+7)/8 C. (exp(1/2)+1)/3 D. (exp(t)+63)/64 E. (exp(t)+1)/4
- Let X have a uniform distribution on the interval (2, 9). Find the probability that the sum of 2 independent observations of X is greater than 16.The probability distribution function of a random variable X is 4. P(X =x)=Dk for x=0,1, 2,3,4 where k is a constant. Determine (a) the value of k. Hence, find P(0Let Y be a discrete random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON