Answer:
y=1/4(x-2)²-5
Step-by-step explanation:
Answer:
a) Marginal probability of X
![f_x(x)=\frac{2}{3}(x+1)](https://tex.z-dn.net/?f=f_x%28x%29%3D%5Cfrac%7B2%7D%7B3%7D%28x%2B1%29)
b) Marginal probability of Y
![f_y(y)=\frac{2}{3}(1+2y)](https://tex.z-dn.net/?f=f_y%28y%29%3D%5Cfrac%7B2%7D%7B3%7D%281%2B2y%29)
c) The probability that the drive-through facility is busy less than one-half of the time is P=0.5.
Step-by-step explanation:
The joint density function of probability is:
![f(x, y) = (2/3) (x + 2y)\\\\0 \leq x \leq 1, \,0 \leq y \leq 1](https://tex.z-dn.net/?f=f%28x%2C%20y%29%20%3D%20%282%2F3%29%20%28x%20%2B%202y%29%5C%5C%5C%5C0%20%5Cleq%20x%20%5Cleq%201%2C%20%5C%2C0%20%5Cleq%20y%20%5Cleq%201)
a) The marginal density of X is
![f_x(x)=\int_0^1 f(x,y)dy=(2/3)(x+2\int_0^1 y\,dy)=(2/3)*(x+y^2)\\\\f_x(x)=(2/3)*(x+(1-0))\\\\f_x(x)=(2/3)*(x+1)](https://tex.z-dn.net/?f=f_x%28x%29%3D%5Cint_0%5E1%20f%28x%2Cy%29dy%3D%282%2F3%29%28x%2B2%5Cint_0%5E1%20y%5C%2Cdy%29%3D%282%2F3%29%2A%28x%2By%5E2%29%5C%5C%5C%5Cf_x%28x%29%3D%282%2F3%29%2A%28x%2B%281-0%29%29%5C%5C%5C%5Cf_x%28x%29%3D%282%2F3%29%2A%28x%2B1%29)
b) The marginal density of Y is:
![f_y(y)=\int_0^1 f(x,y)dx=(2/3)*(\int_0^1x\,dx+2y)=(2/3)*(1^2-0^2+2y)\\\\f_y(y)=(2/3)*(1+2y)](https://tex.z-dn.net/?f=f_y%28y%29%3D%5Cint_0%5E1%20f%28x%2Cy%29dx%3D%282%2F3%29%2A%28%5Cint_0%5E1x%5C%2Cdx%2B2y%29%3D%282%2F3%29%2A%281%5E2-0%5E2%2B2y%29%5C%5C%5C%5Cf_y%28y%29%3D%282%2F3%29%2A%281%2B2y%29)
c) Probability that the drive-through facility is busy less than one-half of the time. This is P(X<0.5).
![P(X](https://tex.z-dn.net/?f=P%28X%3C0.5%29%3D%5Cint_0%5E%7B0.5%7D%5C%2C%282%2F3%29%28x%2B1%29dx%3D%282%2F3%29%5B%280.5%5E2%2B0.5%29-%280%5E2%2B0%29%5D%5C%5C%5C%5CP%28X%3C0.5%29%3D%282%2F3%29%2A%280.75-0%29%3D0.5)
The answer is going to be 6. hope that helped
Answer:
y ≥ 6.25
Step-by-step explanation:
f(x)=4x²+2x-6
positive (4) leading coefficient, curve is left up and right up
x coordinate of vertex: x = - b/2a = - 2/2*4 = - 1/4 (-0.25)
y = 4*(-1/4)² + 2*(-1/4) - 6 = -6 1/4 (-6.25) ... extreme
range: y ≥ - 6.25 [-6.25,∞)
Answer:
O B. 6, 13, 19, 24,
Step-by-step explanation:
because this is the correct answer