For what value of c is the function f(x)=c(7x-(x^2)+8) a probability density function on the interval [0,6]?
For what value of c is the function f(x)=c(7x-(x^2)+8) a probability density function on the interval...
7. A probability density function (PDF) is given by: f(x)-21x3 for x>a What value of 'a' will make this a PDF? 8. A probability density function (PDF) is given by: f(x) k(8x-x2) for 0<x<8 What value of 'k' will make this a PDF? 9. A probability density function (PDF) is given by: f(x)-e.(x4) for x> a What value of a will make this a PDF? 10. A probability density function (PDF) is given by: f(x)-15x2 for-a<x<a What value of a...
8. A probability density function (PDF) is given by: f(x)-k(8x-x2) for 0cx<8 What value of 'k' will make this a PDF? 9. A probability density function (PDF) is given by: f(x)-e.( 4) for x>a What value of a will make this a PDF? 10. A probability density function (PDF) is given by: f(x)-1.5x2 for -acx<a What value of a will make this a PDF?
Decide whether or not the function is a probability density function on the indicated interval. f(x) = *2; 13, 5) No 0 Yes
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval 0<x<2 (a) What is the support of X? (b) Letting S be the support of X, pick two numbers a, b e S and compute Pa<x<b). Draw a graph that shows an area under the curve y = f() that is equal to this probability. (c) What is Fx (2)? Draw a good graph of y=Fx (I). (d) What is EX? (e) What is...
A joint probability density function is given by f(x,y)-c-x(2-x-y), for 0 < x < 1 and 0 < y < 1. Find the value of c to make this a valid density function. A joint probability density function is given by f(x,y)-c-x(2-x-y), for 0
Let X be a r.v. with probability density function f(x)-e(4-x2), -2 < otherwise (a) What is the value of c? (b) What is the cumulative distribution function of X? (c) What is EX) and VarX
Given the probability density function f(x)=14f(x)=14 over the interval [3,7][3,7], find the expected value, the mean, the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation:
Find a value of k that will make fa probability density function on the indicated interval. f(x) = kx, [2, 4] Type an integer or a simplified fraction.)
Verify Property 2 of the definition of a probability density function over the given interval. f(x)=3, [03] Next, determine F(x). First, find the antiderivative off. (3 dx = 3x 3x+C Let C = 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over the far right side of the formula for theprea. 0-0 [0,1] using area =
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...