If X has probability density function f(x) = x/12 on [1,5], find P(1< x < 2).
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![If X has probability density
function f(x) = x/12 on [1,5], find
P(1< x < 2).
А. 1/4
В. 1/8
C. None of these
D. 5/24](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2eebb8b7-983b-4c7c-a379-a90ca654c611%2F179d8544-602e-4fbd-ba8e-e37e774cc5eb%2Fp8ldbzo_processed.jpeg&w=3840&q=75)
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- Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise c=1/2 P(X < 1), Determine whether X and Y are independentSuppose X is a continuous random variable with density f(x) = x/2 , 0 <= x <=2 f(x) = 0 , elsewhere Write an integral expression for the moment generating function M(t).Suppose the joint probability density of X and Y is fX,Y (x, y) = 3y 2 with 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 and zero everywhere else. 1. Compute E[X|Y = y]. 2. Compute E[X3 + X|X < .5]
- For the probability density function f(x) = 3x^2 on [0,1], find: V(X)Suppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y independent?The PDF of a continuous random variable X is as follows: f(X)= c(4x2 - 2x2) 0<* x <* 2 (*less or equal to) a. For this to be a proper density function, what must be the value of c ?
- Find a value of k that will make f a probability density functionon the indicated interval.ƒ(x) = kx; [0, 3]Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?
- The random variables X and Y have the following joint probability density function:f(x,y)={e−x−y , 0<x<∞; 0, elsewhere. What is Cov(X,Y)(X,Y)?Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [2, 4]Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.
