Then P(0 < X < 1/4)=
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- 1) if the amplitudes of X and Y signals have a common probability density function : fxy(x, y) = e^-x/2*y*e^-y^2 x > 0, y> 0 a) find the common sum distribution function (cdf). b) find the probability P[X^1/2 > Y]. c) find marginal probability density functions. 2) problem are the amplitudes of X and Y in D independent of each other? Your answer write in detail, proving it.2.1) Suppose a random variable X has a probability density function in the attached image. a) Find the value of k that makes this a probability density function. b) Find the expected value of X.A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density function
- part a) Write down the joint probability density function fX,Y(x,y) of X and Y on its support.part b) Which values of the constants A, B, C, D, E are correct5. Two random variables X and Y have a joint probability density function 0 < y < x < 2 fxy(x, y) = elsewhere (a) Find the marginal density functions of X and Y. (b) Are X and Y statistically independent?2) X random variable takes value in the range of [0,1] and the probability density function of the random variable is as in the picture. a) Find the constant number a. b) Find the cumulative distribution function of the random variable X. c) Find the probability P (0.5 <X <1).
- Combined probability density function of continuous random variables X and Y -∞<x<∞ , -∞<y<∞ If it is assumed to be defined in the range, which of the following is / are true?Random variable X has the following probability mass function: P(X=x) = (x+1)/12 for x = 0, 1, 2, 5. Based on the PMF, what is P(X> or equal to 2)?