Question * The joint probability density function for X and Y is given by: ((x+y) f(x,y) = x > 0, y > 0,3x + y < 3 2 0. else Then P(0 < X < →) = None of other options 25/32 O 16/27 O 121/256
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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.5. 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?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
- 1)Independent random variables X and Y are exponentially distributed with mean is β . Which of the following is the expected value of the new random variable Z defined by Z = X + Y? 2)The composite probability density function for the random variables X and Y is given as f (x, y) = x + y, 0 <x <1, 0 <y <1, otherwise 0. Which of the following is the value of the probability P (X ≤ 1/2)?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 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?
- 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)?a. Explain the difference between the method of moment generating function and the method of incarnation to find the probability density function of a random variable b. Let X1, X2, X3 ,,,,, each of them has Poisson distribution with parameter lamda 1, lamda2, lamda3,........ i. Get the probability distribution of Y=X1+X2+....Xn ii. Get the mean and variance of Y c. Y1 and Y2 be a joint probability function as shown below in the screenshot imageU=Y1/(Y1+Y2), Using the method of incarnation (Jacobian), find the probability density function of USuppose X and Y have joint probability density function ?(x, y) = { 6x, 0 < x < 1, 0 < y < 1 − x 0, elsewhere. a. Determine whether the two random variables are dependent or independent. b. If the value of Y is 0.5, what is the probability that X will have a value greater than 0.3? Please answer this question step by step and justify your solution
- 5)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find a sufficient statistics for θ. Check if the statistics you have found are minimally sufficient.1. 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. 2. Suppose the lifetime of a particular type of old mobile, X, can be modelled by the probability density function f(x) = 0.5 e −0.5 x; x ≥ 0. Suppose that you just bought 5 old mobiles, what is the probability that at least 3 of the mobiles will survive less than 2 years?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 correct