Question 2: The support of a continuous random variable is the set of the outcomes such that f(z)...
Question 2: The support of a continuous random variable is the set of the outcomes such that f(x)> 0. If X has support la, b) and Y support [c, d what is the support of X + Y?
1. Let X be a continuous random variable with CDF F(ro)-a+b 3 and support set 0, 1]. (a) Calculate the values of a, b that would make F(ro) a valid CDF. (b) Write out the pdf of X. c) Calculate EX d) Calculate EX
Random variable
(20) Z X+Y is a random variable equal to the sum of two continuous random variables X and Y. X has a uniform density from (-1, 1), and Y has a uniform density from (0, 2). X and Y may or may not be independent. Answer these two separate questions a). Given that the correlation coefficient between X and Y is 0, find the probability density function f7(z) and the variance o7. b). Given that the correlation coefficient...
2. A continuous random variable has joint pdf f(x, y): xy 0 x 1, 0sys 2 f(x, y) otherwise 0 a) Find c b) Find P(X Y 1) b) Find fx(x) and fy(v) c) Are X and Y independent? Justify your answer d) Find Cov(X, Y) and Corr(X, Y) e) Find fxiy (xly) and fyixylx)
Probability and statistics for engineers
d. 045 Question 2 Not yet answered A continuous random variable X has the following density function (2x+1) f(x)= 1<x<3 10 Find 0. otherwise PC 2 < x < 2.5) Marked out of 2 P Flag question a. 0.275 b.0.1 C 0.05 d. 2.13 3 Let A and B two independent events and PIA) - 0.6 and PAB) =
(6) Suppose that X is an absolutely continuous random variable with density 1<I<2 f(3) = lo, otherwise. Find (a) the moment generating function MX(t). (b) the skewness of X (c) the kurtosis of X (7) Suppose that X, Y and Z are random variables such that p(X,Y) = 1 and p(Y,Z) = -1. What is p(X, Z)? Explain your answer. (8) Suppose that X, Y and Z are random variables such that p(X,Y) = -1 and p(Y,Z) = 0. What...
4. et X be a continuous random variable with support (0, 2) and PDF defined by f(x) = ( cx3 0 < x < 2 0 otherwise. a) Compute E[X]. b) Compute V ar(X)
Let f be the pdf on a continuous random variable Z. The variance ofZ is given by σZ and the pdf is symmetric (f(x) = f(−x)) and everywhere positive.Define another random variable X as X = α3Z3 + α2Z2 + α1Z + α0.(i) For which values of αi are X and Z uncorrelated?(ii) For which values of αi are X and Z independent?
1. Let X be a continuous random variable with support (0, 1) and PDF defined by f(x) = ( cxn 0 < x < 1 0 otherwise, for some n > 1. a) Find c in terms of n. b) Derive the CDF FX(x).
Recall from class that the standard normal random variable, Z, with mean of 0 and stan- dard deviation of 1, is the continuous random variable whose probability is determined by the distribution: a. Show that f(-2)-f(2) for all z. Thus, the PDF f(2) is symmetric about the y-axis. b. Use part a to show that the median of the standard normal random variable is also 0 c. Compute the mode of the standard normal random variable. Is is the same...