If the random variables X and Y have the joint density for 1 ≤ x + y ≤ 2, x ≥ 0, y ≥ 0 f(x, y) = 0 otherwise, what is the probability P[max(X, Y) > 1] ? 67
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complete solution
![If the random variables X and Y have the joint density
x for 1<x+y ≤ 2, x ≥ 0, y ≥ 0
f(x, y) =
0
otherwise,
what is the probability P[max(X,Y) > 1] ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7da3d53-31d2-48e7-b787-228d47eca939%2F77d31fd8-1904-492e-9227-0b4f036088ae%2Fniz1rwk_processed.png&w=3840&q=75)
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- Suppose that X is a random variable with density and suppose that ?=e(-4X) Determine ?(?)Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?If the joint density of the random variables X and Y is حل سؤال الثاني في ورقه
- If X is a continuous random variable find the CDF and density of the function y = x/3Suppose the random variables X and Y have joint probability density function f(x,y) given by: (image)Find: P(X < Y) = fX|Y=y (x)If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.
- Show that if a random variable has a uniform density with parameters α and β, the probability that it will take on a value less than α+p(β-α) is equal to p.Suppose that the random variables X and Y have a joint density function given by: f(x,y) = {c(2x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise P(3 < X < 5, Y >1), P(X < 3), P(X +Y > 5), Find the joint distribution function (cdf),A point D is chosen on the line AB, whose midpointis C and whose length is a. If X, the distance from D toA, is a random variable having the uniform density withα = 0 and β = a, what is the probability that AD, BD,and AC will form a triangle?