1. Consider the function f(x) = = (x² - 1), 0, 1

Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

A:

Q: Find f. f "(x) = x-2, x > 0, f(1) = 0, F(3) = 0 %3D %3D In (1) |-In(\x|) + In(1)x + f(x)

A: Given f"(x) = x-2     ,   x>0   f(1) =0   , f(3)=0

Q: find the area between f(x)=x2+2 and g(x)=-x+1 on [1,3]

A: Draw the graph. To find the region between the red and blue function: Red: y=x2+2 Blue: y=-x+1…

Q: Let X­­1 ~ Binomial(n1, p), and let X2 ~ Binomial(n2, p), independent of X1.  Show using a discrete…

A: It is given that: X­­1 ~ Binomial(n1, p) X2 ~ Binomial(n2, p) Y = X1 + X2

Q: The joint pdf of Y, and Y, is given by (a) ,with support (b) , and 0 elsewhere. (a) 1/y2; (b) 0 < y…

A:

Q: How to find the median with an integral when f(x)=4(1-2x) on the interval [0,1/2]

A: Consider that a continuous random variable X has a probability density function f(x), over the…

Q: Let - fot² Find the average value of f on the interval [0, 1]. f(x) = dt.

A: Given: The function is fx=∫1xet2dt. To find: Average value of fx=∫1xet2dt on the interval 0,1.…

Q: 6. If f(x,y) = 2 x>0; y>0; x+y<1 Show the conditional pdf of Y given x is uniform.

A: