find the probability density of W=Y-X
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These two questions are given me sleeplessness. Please help me. Thanks
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- Numbers X and Y between 0 and 1 are chosen randomly. The joint probability density is p(x, y) = 1 if 0 < x < 1 and 0 < y < 1, and p(x, y) = 0 otherwise. Calculate the probability P that the product XY is at least ½.1. 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…4. A continuous random variable x that can assume value between x = 2 and x = 5 has a density function given by f(x) = 2/27 (1 + x). Find a) P (x < 4) and b) P (3 < x < 4)
- (a) A continuous random variable X has density f(x), where f(x) = 0 for x < 1and f(x) = k/x3for x ≥ 1. Find the value of k.(b) Find all β for which E(X^β) exists. I don't really understand what the sort portion of the question is asking.1)A random vector z = (x y) T has joint probability density given by:a)Sketch the graph of the probability density function pxy(X, Y ).b)Determine the value of the constant C.c)Determine the mean mz vector.25. Let X be a continuous random variable with density function f (x) = 32 x 2, −1 ≤x ≤ 1. Sketch this density function. Use the central limit theorem to sketch the approximate density function of S = X1 +···+ X50, where the Xi areindependent random variables with density f . Similarly, sketch the approximate density functions of S/50 and S/√50. For each sketch, label at least threepoints on the horizontal axis
- 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.The random variable X has probability density function f where f(x)=\ ( kx(x + 1) (2-x ), 0 <= chi <= 2 ,;0, otherwise) ( a) Sketch the graph of the function. You are not required to find the coordinates of the maximum. (b) Find the value of k1) 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.
- The joint density function of the continuous variables X and Y is fX,Y(x,y) = 7.5x(2-x-y) for 0<X<1 and 0<Y<1. (a) Find the expected value of X+Y. (b) Find fX(x), and fY(y). (c) Find Cov(X,Y). (d) Find Corr(X,Y).A sharpshooter is aiming at a circular target withradius 1. If we draw a rectangular system of coordinates with its origin at the center of the target, the coordinates of the point of impact, (X, Y), are random variables hav-ing the joint probability density f(x, y) =⎧⎪⎪⎨⎪⎪⎩1π for 0 < x2 + y2 < 10 elsewhere Find(a) P[(X, Y) ∈ A], where A is the sector of the circle inthe first quadrant bounded by the lines y = 0 and y = x;(b) P[(X, Y) ∈ B], where B = {(x, y)|0 < x2 + y2 < 12Let X have a probability density function A) Let Y = X1 + X2 + … + X25 be the sum of a random sample of size 25 from the distribution whose pdf is f(x). Approximate P[12 < Y < 21]. B) Let Yn = X1 + X2 + … + Xn be the sum of a random sample of size n from the distribution whose pdf is f(x). Discuss lim n->infinity P[-14.4 < Yn < 28.8]
