Probability Density Function and Marginal Density

2. The joint pdf of X and Y is given by f(x,y)= c(y² - x²)x^(-y), -y ≤ x ≤ y, y>0. a) What is the marginal density of Y? b) What is the value of c? c) What is E(Y)?

Jointly Distributed Random Variables : Joint Density

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.

Jointly Distributed Random Variables : Binomial Distributions

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 ...continues

Jointly Distributed Random Variables : Gamma and Exponential Distributions

If X1, X2,...Xn are all independent Expo(λ), and Sn=Σ i=1..n Xi, then Sn≈Gamma (n,λ). Show that this is true when n=2. Please see attached.

Jointly Distributed Random Variables : Joint Density and Conditional Density

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.

Jointly Distributed Random Variables : Probability and Cumulative Density Functions

Let X and Y be 2 independent 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?

Jointly Distributed Random Variables : Joint Probability Density Functions

Suppose X and Y are jointly continuous with joint pdf f(x,y)=xe^[-x(1+y)], x,y>0. a) What are the marginal pdf's of X and Y? b) What is the conditional pdf of X given Y=y? c) What is the conditional pdf of Y given X=x? d) What is the distribution of Y given X=x called?

Jointly Distributed Random Variables : Expressions for Density Functions

Suppose X and Y are continuous random variable, X and Y are independent and that x>0 and y>0. The pdf of X is Fx(X) and the pdf of Y is Fy(Y). Find the expressions for the density function of Z in terms of fx and fy, if... a) Z=X/Y b) Z=XY

Stat Class

#4. Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). a. What are the 16 outcomes in the sample space? b. Which outcomes are in the event that exactly three of the selected mortgages are fixed rate? c. Which outcomes are in the event that all four mortgages are of the same type? ...continues

Probability : Binomial Distribution

#34. A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in depth interviews. Suppose the selection is made in such a way that any particular group of 6 workers has the same chance of bein ...continues