Suppose X and Y are independent random variables. X is uniformly distributed on (0, ) and Y is exponentially distributed with 1=2. Find the joint density function f(x,y) of X and Y.
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- Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.Be X a random variable with density function defined by f(x) = -2², , x>0. 3 Get the moment-generating function and based on it, calculate the average and variance of X.Suppose that X and Y have a joint probability density function given by ce-3z-5y if r, y 20 fx.x(T, y) = otherwise Are the random variables X and Y statistically independent? Justify your answer.
- Let X and Y be two random variables that are independent and have the same probability density function. If U = max (X, Y) V = min (X, Y), find the distribution function of the U random variable using the distribution function technique.Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.The life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772
- Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X + 25. Then what is the probability density function of Y (fy(y)). Probability TheorySuppose that the random variable X has density fx (x) = 4x³ for 0 X).Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1], and f(x,y)=0,elsewhere. Find the expected value of the random variable Z = 10X+14Y.
- The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by 2e-(x+2y) X> 0, γ> 0 fx,ylx,v) = { else Then the probability that the first transistor last for at least half hour given that the second one lasts at least half hour equals Select one: a. 0.7772 b. 0.3935 10 c. 0.606 d. 0.6318 e. 0.3669Suppose that X is a random variable whose density function is defined as follows: (a+1) 2a fx(x) = 2a+1 with 0 -1. For a = 1.15 calculate the IQR of X.Let X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.