((x+ y) f(x,y) = x > 0, y > 0,3x + y< 3 else Then P (0 < x < ;) = O 121/256 O None of other options 25/32 O 16/27
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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?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
- 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?Two discrete random variables X and Y have the joint probability density function: f(x.y)=e*p" (1-p)* y!(x-y)! x-y ,y 0,1,2,..,x; x 0,1,2,... where 2, p are constants with 2 >0 and 0 <p<1. 1. Find the marginal probability density functions of X and Y. 2. Find the conditional distribution of Y for a given X and of X for a given Y.1. Suppose that a continuous probability function has a density curve, and 25.6% of the area under this density curve is shaded. What probability does that shaded region represent? Probability (give your answer as a decimal): 2. Express the region that is described below as a probability. The area under a continuous density curve between x=−1.21x=-1.21 and x=1.96x=1.96 , where the horizontal axis is scaled in units of the random variable xx . P(−1.21<xorx<1.96)P(-1.21<xorx<1.96) P(1.96<x<−1.21)P(1.96<x<-1.21) P(x<−1.21or1.96<x)P(x<-1.21or1.96<x) P(x<−1.21and1.96<x)P(x<-1.21and1.96<x) P(−1.21<x<1.96) 3. The time it takes me to wash the dishes is uniformly distributed between 6 minutes and 16 minutes.What is the probability that washing dishes tonight will take me between 10 and 14 minutes?Give your answer accurate to 2 places after the decimal point, if necessary. 4. A bank's loan officer rates applicants for credit. The…
- 1. ELT(Let) Y be a random variable with the probablility function defined by this picture 1.1 find the cumulative distribution func. of the random variable Y 2 ELT(Let) the joint probabilty density function of two con random variable Y and X (Other picture fx,y) 2.2 find P(1<y<=2)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).