Let Xa random variable with density function f (x) = e-® . 1(0,00) (2). Determine tha density function of Y %3D 1+X

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Q: (ii) Let the random variable, y have probability density function, kye-0.5y f(t) = { , y 2 0…

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A: The Gamma distribution is defined as follows :

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A: Step 1:Step 2:Step 3:Step 4:Option(E) : correct

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Q: 24. Consider a distribution with density on the interval [0, 2]. Let the probability density…

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A: The pdf of random variable X is given: fX(x) = θ xθ-1,   0≤x≤1

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Q: Show that k = O Show that the cumulative distribution function is |y² F(y) = 12 (y² + 2) ) 0 2.…

A: To find the value of k, we will use the fact that ∫-∞∞fydy=1 The cumulative distribution function is…

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A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

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A: Given that, the probability density function of X is

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Q: Find the probability density of the sum W = X+ Y.

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Q: One recognizes the integrand of Equation (23) as a r(a, 6) density, hence M (t) = (;)"(1) = (24) |3|…

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Q: Calculate the 30th percentiles of X. (Round to 2 decimals).

A: The density function is, fx=2.52002.5x3.5        for x≥2000                          otherwise The…