Independence of Random Variables and Distribution Connections

Independence of random variables

Sums of independent Binomials

Bridges between Binomial and Hypergeometric

A joint PMF has P(X = 1, Y = 2) = 0, while P(X = 1) = 0.4 and P(Y = 2) = 0.25. What follows?

X is Binomial(5, 0.4) and Y is Binomial(3, 0.4), independent. What is the distribution of X + Y?

X and Y are independent with P(X = 1) = 0.3 and P(Y = 2) = 0.6. What is P(X = 1 and Y = 2)? Enter a decimal like 0.18.

A joint PMF gives P(X = 2, Y = 1) = 0.15 and P(X = 2, Y = 2) = 0.10, and these are the only cells with X = 2. What is P(X = 2)? Enter a decimal.

A jar holds 1000 marbles, 400 red. You draw 5 without replacement and count reds. The Hypergeometric is exact, but a Binomial approximation with p = 0.4 is excellent here. Its parameter n is what integer? Enter the integer.

In your own words, state the most important definition, theorem or method of this lesson and explain what it says.