If X has an exponential distribution with the param-eter θ, use the distribution function technique to find the probability density of the random variableY = ln X.

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A: For finding median through probability density function we use: ∫0Mf(x).dx = 12 M: Median value

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A: Given the joint probability density function, PX&lt;1, Y&lt;12=∫01/2ce-4y∫x=y1e-8xdxdyPX&lt;1,…

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Q: (a) Give the marginal density functions for both random variables. Are the independent? (b) What is…

A: f(x,y)=ye-y(1+x)        x,y&gt;0

Q: Suppose that the random variable W has a beta distribution with probability density function f (w)…

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Q: Suppose that the random variable W has a beta distribution with probability density function f(w)…

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Q: The probability density function of the random variable X is given by: Sce-2x 0 f(x)= = for x > 0…

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Q: If X has an exponential distribution with parameter 0, use the distribution function techniques to…

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Q: Suppose that the random variable W has a beta distribution with probability density function f(w)…

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Q: A continous random variable has density function f(x)=(3x2)/(03) for Osxse, for some 0>0, and zero…

A: First we have to determine mode and median of given distribution.

Q: Let X be a uniformly distributed random variable with probability density function: sa -1 <x < 3…

A: Given , Y= x2 = g(x) Then g-1(y)= = √Y diff. it w.r.t. Y, d/dy g-1(y)= 1/2√y We know that,  P.d.f.…

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Q: The lifespan of a light bulb is expected to follow a Weibull distribution, a = 3 and 8 = 8.5, with a…

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Q: Consider a probability density function for a random variable X, defined by for 1 < x < 3 f(x) = 16…

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Q: A random variable X has the probability density function (pdf) shown in he figure below. fx (2)

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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Q: Let X be an exponential random variable with the following probability density functioi x20 f(x;2)={…

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Q: Let X be a random variable with the probability density function, Oe-ex 0 < X < ∞; f (x) = { 0,…

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