Find the marginal density h(y) for the joint density function. Find the conditional density f(y/x). Find the conditional density f(x/y).
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- By the end of 2021, the percentage, ?, of the population (expressed in decimals) that will be vaccinated is given by the density function a. Find ?. b. Find the cdf ?(?) and use it to evaluate the probability that 30% to 60% will be vaccinated at the end of the year. Please answer this step by step and justify your answer.Given the density function f(x) = 2(1 − x), for 0 < x < 1, = 0, otherwise. Find the standard deviationIf Θ ∼ Uniform(a = 0, b = 3), find the probability density function of sin(Θ).
- In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. The data show that the density function of these time gaps was given approximately by p(t)=ae−0.119t where t is the time in seconds and a is a constant.Find the constant a.Given the function below, solve for the following:F(y) = {y/6, −2 < y < 4 0, elsewherea. Verify that f(x) is a density function. b. Find the cumulative distribution function. c. List the cumulative distribution function. d. Draw the Probability Mass Function PlotThe life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2 for x in [0,∞). Find the probability that a randomly selected laptop battery will last between 2 and 5 years?
- Given that the joint probability density function is f (x, y) = 2 ; 0<x<y<1, find the probability of P (0<X<1/2, 0<Y<1/2). Next, find the conditional density function of Y given X for 0<X<1 , h(y|x).Could you show me step by step how to find the density function? •The answer should be f(x)=1/2u•exp^-x/(2u) It should be an exponential distribution, but why?Show that the following are probability density functions (pdf’s): b. f2(x) = 2e−2xI(0,∞)(x)