Probability Class - Introductory 400 Level - Jointly Distributed Random Variables

The joint density of X and Y is given by... Are X and Y independent? What if f(x,y) were given by...? Please see attached.

Probability Class - Introductory 400 Level - Jointly Distributed Random Variables

Suppose that 25% of US males and 23% of US females never eat breakfast. Suppose a random sample of 250 men and 250 women is taken and polled about eating breakfast. a) What is the probabilty that at least 110 of these 500 people never eat breakfast? b) What is the probability that the number of women who never eat breakfast is at least as large as the number of men who never eat breakfast?

Probability Class - Introductory 400 Level - Jointly Distributed Random Variables

If X1, X2,...Xn are all independent Expo(λ), and Sn=..., then Sn≈Gamma (n,λ). Show that this is true when n=2. Please see attached.

Probability Class - Introductory 400 Level - Jointly Distributed Random Variables

The joint density function of X and Y is given by f(x,y)=xe^[-x(y+1)], x>0, y>0. a) Find the conditional density of X, given Y=y and that of Y, given X=x. b) Find the density function of Z=XY.

Probability Class - Introductory 400 Level - Jointly Distributed Random Variables

Let X and Y be 2 independant continuous random variable with X≈U(1,3) and Y≈(0,2). Define U=X+Y (a) What is the pdf of U? (b) What is the cdf of U?