1. Consider the following function: 4x 0<x<0.5 f(x)= 4- kx 0.5 <x<1 0 Otherwise a) (5%)...
1. The density function of b is given by kx(1 - x) f(x) = { for 0 < x 51, elsewhere. (a) Find k and graph the density function. (b) Find P(1/4 < ſ < 1/2). (c) Find P(-1/2 sã < 1/4). (d) Find the CDF and graph it. (e) Find E( ), E(52), and V(5). 1. The density function of ğ is given by |kx(1 – x) o for 0 < x 51, elsewhere. f(x (a) Find k and...
QUESTION 4 Consider the CDF 0 у<0 0.5 F(y) = 0.75 0.90 Osy<2 2sy<3 3sy<5 1 Y>5 Find pſy=5) O A. 0.10 B. 0.15 C. 0.25 D.0.25 QUESTION 5 Consider the PM.F
[4+3+3 Points] 9. For the following probability density function, f(x) -k for 0 <x < 0.5 f(x) - 3x2 for 0.5 < x < 1 f(x) -0 otherwise What is the value of k? Find the median value of x Find the probability that X<0.75 a. b.
1) Let X and Y have joint pdf: fxy(x,y) = kx(1 – x)y for 0 < x < 1,0 < y< 1 a) Find k. b) Find the joint cdf of X and Y. c) Find the marginal pdf of X and Y. d) Find P(Y < VX) and P(X<Y). e) Find the correlation E(XY) and the covariance COV(X,Y) of X and Y. f) Determine whether X and Y are independent, orthogonal or uncorrelated.
4. Consider the probability density function (x)for x>0, and zero otherwise. Determine a. The value of a b. P(X> 22) C. e The value of x such that P(X<x)-0.1
1. Given f(x) = kx(9 - x2)4 0<x<3, otherwise a) Find k. f(x) 20 a pdf pro b) Calculate F(x) and the three quartiles. c) Calculate E(X2) and Var(x2). d) Calculate E(X) and Var(x). (needs more than calc 1) (Bonus)
The density function of X is given by f(x) = a + bx2 if 0 ? x ? 1 0 otherwise. Suppose also that you are told that E(X) = 3/5. (a) Find a and b. (b) Determine the cdf, F(x), explicilty. Problem 4. The density function of X is given by f(z) = 0 otherwise. Suppose also that you are told that E(X-3/5. (a) Find a and b. b) Determine the cdf, F(r
f(x) = 3x, 0<x<1 0, otherwise Problem 9: Find the CDF of X, [4] Problem 10: Find P(X < 1/3) [4] Problem 11: Find the 95th percentile of X (Remark: You have to solve for x in the equation P(X < x) = .95) [4] Problem 12: Find P(X > 2/3|X > 1/3) [4] A pipe-smoking Mathematician carries two match boxes, box A in his left hand and box B in right-hand pocket. Initially, each box contains 3 matches. Each...
is a continuous random variable with the probability density function (x) = { 4x 0 <= x <= 1/2 { -4x + 4 1/2 <= x <= 1 What is the equation for the corresponding cumulative density function (cdf) C(x)? [Hint: Recall that CDF is defined as C(x) = P(X<=x).] We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...
Consider the following pdf: ; 0<x<1 f(x)-2k ; l<x<2 0 otherwise (i)Determine the value of k. (ii) Find P(X 0.3) (iii) Find (0.1 〈 X 1.5).