Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)
f(x) =cx^-3 for 1<x<infinity, find E(X) I believe c=2
7. Let S = [0, 1] × [0, 1] and f : S → R be defined by f(x, y) = ( x + y, if x 2 ≤ y ≤ 2x 2 , 0, elsewhere. Show that f is integrable over S and calculate R S f(z)dz.
7.30 Given the probability density function 20x3 (1- x) for 0< f(x) <1 and 0 elsewhere find the following: The cumulative distribution function F(x) b. Е(X) Find Pr(0.5 <X < 2). a. d. SD(X) с. Е(X?) e. 7.30 Given the probability density function 20x3 (1- x) for 0
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
7.2 Let X have density f(x) = cx for 0 < x < 2 and f(x) = 0 for other values of x. a. What is c? b. What is F(x)? c. What are E[X] and Var[x]? 7.3 Let X have density f(x) = cx(1 - x) for 0 sxs 1 and f(x) = 0 for other values of x. a. What is c? b. What is F(x)? c. What are E[X] and Var[x]?
2. Let X be a continuous random variable with pdf ( cx?, [xl < 1, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2) Suppose that X has density function f(a)- 0, elsewhere Find P(X < .3|X .7).
Suppose X is a random variable whose density is f(x) = cx(1 - x) for 0 < x < 1, and f(x) = 0 otherwise. Find a. the value a c. b. P(X <= 1/2). c. P(X <= 1/3)
(1 point) Find a polynomial of the form f(x) = ax’ + bx² +cx +d such that f(0) = -3, f(-2) = 5, f(-3) = 2, and f(4) = 5. Answer: f(x) =