(5) 5. If X is uniformly distributed on [ - 1,1], find the cdf and pdf...
Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c) Find the joint PDF of Y and Z.(: Try the trick in Problem 2(b) Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c)...
Show the random variables X and Y are independent, or not independent Find the joint cdf given the joint pdf below Suppose that (X, Y) is uniformly distributed over the region defined by 0 sys1-x2 and -1sx 4 Therefore, the joint probability density function is, 0; Otherwise Suppose that (X, Y) is uniformly distributed over the region defined by 0 sys1-x2 and -1sx 4 Therefore, the joint probability density function is, 0; Otherwise
2X x 20 5 pt. a. Find the cdf and pdf of Y in terms of the cdf and pdf of X. of Y when X is a Gaussian random variable with zero mean and variance-4
Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2. (a) Find the CDF and PDF of Y =X1 + 2X2 . (b) Find the CDF of Z = Y + X3 . (c) Find the joint PDF of Y and Z . (Hint: Try the trick in Problem 2(b))
probability question Suppose that X has a pdf f (x)--for 1 identically distributed copies of that variable. Find the cdf, pdf and expected value of minimum of this set of variables. oo. Let(Xinl be a collection of independent and x x4 Suppose that X has a pdf f (x)--for 1 identically distributed copies of that variable. Find the cdf, pdf and expected value of minimum of this set of variables. oo. Let(Xinl be a collection of independent and x x4
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0
X and Y are jointly uniformly distributed and their joint PDF is given by: fX,Y(x,y) = {k , 0<=x<=4, 0 <=y <= 8 0 , otherwise } a.) find the value of k that makes the joint PDF valid b.) compute the probability P[(X-2)^2 + (Y-2)^2 < 4] c.) compute the probability P[Y > 0.5X + 5]
2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf of Y
a. Find the cdi and pdf of Y in terms of the cdf and pdf of X 3 pt. b. Find the pdf of Y when X is a Gaussian random variable with zero mean and unit variance 3 pt.
2 pts 5 pt. Find the cdf and pdf of Y in terms of the e Find the pdf of Y w df and p df of X - -L hen X is a Gaussian random variable with zero mean and varia ㄟ ill he heavy