Let the distribution probability of random variable (x, y) be f (x, y) = 3x (0)

Let the distribution probability of random variable (x, y) be f (x, y) = 3x (0)

The range of Z is 01) 3xdx ∫ (x-z -- > x)
The former result is Z ^ 3, and the latter is (3 / 2) Z - (3 / 2) Z ^ 3
So f (z) = (3 / 2) Z - (1 / 2) Z ^ 3
The density function f (z) = DF (z) / DZ = (3 / 2) (1-z ^ 2) is obtained by derivation

Two dimensional random variables X, y obey (0,1) uniform distribution, z = max (x, y)
Is to find z = max (x, y) distribution function
Please write down the specific steps

F(X)=(X-0)/(1-0)=x/1=x
F (y) = (y-0) / (1-0) = Y / 1 = y and above are two uniform distribution functions
F(Z)
=F(MAX(X,Y))
=1-(1-F(X))(1-F(Y))
=1-（1-X/1)(1-Y/1)
=1-(1-x)(1-y)
=1-(1-x-y+xy)
=x+y-xy
When we calculate max (x, y), we can imagine two parallel resistors. When the two resistors are damaged at the same time, the circuit will be disconnected, so the probability of normal operation of the circuit is 1-p {simultaneous damage}, and P {simultaneous damage} = P {1 damage} * P (2 damage) = (1-p (1 normal)) (1-p (2 normal))
So f (max (x, y)) = 1 - (1-f (x)) (1-f (y))

Given the distribution law of random variable (x, y), find the distribution law of V = max {x, y}

Z = max (x, y), because X and y are independent and identically distributed, the possible value of Z is 0,1p (z = 0) = P (max (x, y) = 0) = P (x = 0, y = 0) = P (x = 0) P (Y = 0) = 1 / 4P (z = 1) = 1-p (z = 0) = 3 / 4 (this is calculated by using the probability of opposite events, if the direct calculation is p (z = 1) = P (max (x, y) = 1) = P (x = 0, y = 1) + P (x = 1

Probability theory problem: random variables x1, X2 are identically distributed, and P (x1 = - 1) = P (x1 = 1) = 1 / 2, P (x1 = 0) = 1 / 4, and P (x1x2 = 0) = 1
Then p (x1 = x2) = ()
A.0 B.1/4 C.1/2 D.1

P(X1=-1)=P(X1=1)=1/2 P(X1=0)=1/4-->
X1 -1 0 1
p 1/4 1/2 1/4
The joint distribution is
X2\X1 -1 0 1
-1 △ ◇ △
0 ◇ ◇ ◇
1 △ ◇ △
P (x1x2 = 0) = 1 --- > deduces that the sum of the middle five} is 1, and by the joint distribution property, the horizontal line} plus the vertical line} is 1, deduces that the middle line} = 0, and deduces △ = 0 by symmetry, the edge line} = 1 / 4, and then deduces △ = 0, so the answer a