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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) 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).A random variable X has the probability density function defined by f(x) = kx, 0 ≤ x ≤ 2. a. Find P(X>1). b. What is the probability density function of Y = 8X2? c. What is the expected value of Y?
- 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 correctdistribution f(x) given-3 < x < -2 ------> c * x + 3 2 < x < 3 -------> 3 - c * x 0 elsewherefind the value of c so that f(x) is a valid probability density function5. 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?
- continuous random variable has probability density function given by F(x) =k(2x+3) 1<=x<=2 0 ,otherwise Find k if f(x) is a probability density functionFind Value of k P(1.5<=x<=4) ?The probability density function of the X random variablelike this.a. The probability of a random variable U defined as U = X^2Find the density function.b. V = 1/X Find the probability density function of the random variable V defined as.The random variable X has a uniform density function over the interval [-1, 1]. a. Sketch the probability density function of X. Find the mean and variance 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 functionA random variable X has density function (pdf). Find c a) Find the cumulative distribution function FX(x) (cdf) of X. b)Find E[X]. c)Find V ar[X].A random variable Y has a probability density function f(y) = A(y − 1.5) over the state space−2 ≤ y ≤ 3, where A is a constant. Calculate the median of the random variable Y.