Joint Probability Function f(x,y)= 3 2 3 [AQ] y 8 5 5-x-y , x = 0, 1, 2, 3; y = 0, 1, 2; 2≤x+y≤5
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From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 5 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample, the joint probability distribution of X and Y is given by the accompanying
What is PXY equal to?
![Joint Probability Function
f(x,y)=
3
2
3
[AQ]
y
8
5
5-x-y
, x = 0, 1, 2, 3; y = 0, 1, 2; 2≤x+y≤5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3eb03a80-7cae-4d33-b228-e2e0361c370e%2F116aad51-a84b-4ef2-aeeb-2559c76609d4%2F2lo0ej_processed.png&w=3840&q=75)
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- X1, X2 are independent continuous random variables with a uniform distribution in the interval (a, b). Calculate the moment generating function, expected value, variance of random variable Y = X1 + X2Let Y be a continuous random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2X and Y are continuous random variables with pdf f(x,y) = 2x for0 ≤x ≤y ≤1, and f(x,y) = 0 otherwise. Find the conditional expectation ofY given X = x.
- IF F(x, y) is the value of the joint distribution function of X and Y at (x, y), show that the marginal distribution function of X is given by G(x) = F(x, ∞) for - ∞ <x < ∞ Use this result to find the marginal distribution function of X for the random variable F(x, y) = { (1-e-x^2 ) (1- e-y^2) for x>0, y> 0 and 0 elsewhereDetermine the value k so that the given function can serve as a probability distribution of the discrete random variable X: f(x) = k(x2 + 4), for x = 0, 1, 2, 3. Use 4 decimal places.True or False; For a continuous random variable X, P(X=x) = f(x) 1. True 2.False
