From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. Suppose X is the number of oranges and Y is the number of apples in the sample.(a) Find the joint probability distribution of X and Y.(b) Find P[(X,Y)EA], where A is the region that is given by {(x,y) | x+y<3}.C(a) Complete the joint probability distribution below.(Type integers or simplified fractions.)Xf(x,y)034y02 A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, andsuppose that the joint density function of these random variables is as shown below. Complete parts (a) through (c).(6x +5y), 0≤x≤ 1,0 sys1f(x,y)=0,elsewhere(a) Find the marginal density of X.Select the correct choice below and fill in the answer box to complete your choice.O A. h(y) =for 0 ≤ y ≤ 1O B. g(x)=for 0≤x≤ 1

Given that As per the guidelines I answered the first question

From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. Suppose X is the number of oranges and Y is the number of apples in the sample. (a) Find the joint probability distribution of X and Y. (b) Find P[(X,Y)EA], where A is the region that is given by {(x,y) | x+y<3}. C (a) Complete the joint probability distribution below. (Type integers or simplified fractions.) X f(x,y) 0 3 4 y 0 2

From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. Suppose X is the number of oranges and Y is the number of apples in the sample. (a) Find the joint probability distribution of X and Y. (b) Find P[(X,Y)EA], where A is the region that is given by {(x,y) | x+y<3}. C (a) Complete the joint probability distribution below. (Type integers or simplified fractions.) X f(x,y) 0 3 4 y 0 2

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

See similar textbooks

Similar questions

Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.
From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample, find (a) the joint probability distribution of X and Y ; (b) P [(X, Y ) ∈ A], where A is the region that is given by {(x, y) | x + y ≤ 2}.
In a box of gadgets containing 3 Samsung phones, 2 iPhones, and 3 Google Pixelphones, a random sample of 4 phones is selected. If X is the number of Samsung phonesand Y is the number of iPhones in the sample, a. the joint probability distribution table of X and Y;b. P[(X, Y ) ∈ A], where A is the region that is given by {(x, y) | x + y ≤ 2}.c. f(y|x=2) for all values of y (tabulate);d. P(X = 0 | Y = 2).
From a sack of fruit containing 3 bananas, 3 apples, and 3 oranges, a random sample of 4 pieces of fruit is selected. Suppose X is the number of bananas and Y is the number of apples in the sample. (a) Find the joint probability distribution of X and Y. (b) Find P[(X,Y)∈A], where A is the region that is given by {(x,y) | x+y≤3}.
In a box of gadgets containing 3 Samsung phones, 2 iPhones, and 3 Google Pixel phones, a random sample of 4 phones is selected. If X is the number of Samsung phones and Y is the number of iPhones in the sample, find: a. the joint probability distribution table of X and Y;b. P[(X, Y ) ∈ A], where A is the region that is given by {(x, y) | x + y ≤ 2}.c. f(y|x=2) for all values of y (tabulate);d. P(X = 0 | Y = 2).
If the random variable X and Y are independent of each other. X~N(0,1) and the probabilitymass function of Y is P(Y=0)P(Y=1)=1/2. If Fz(z) denotes the cumulative distribution functionof random variable Z=XY, then the number of discontinuites of function Fz(z) is
The joint probability function of two discrete random variables X and Y is given by Ax,y) = c(2x+y), where x and y can assume all integers such that 0< x
From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample, find (a) the joint probability distribution of X and Y ;(b) find E(X2Y − 2XY );(c) find μX − μY .
Show that if X is a random variable with continuous cumulative distribution function F(x), then F(x)=U is uniformly distributed over the interval (0,1).
From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample: a. Find the joint probability distribution function(x,y). b. Create the joint probability distribution table for X and Y. c.Find P [(X, Y) € A], where A is the region that is given by {(x,y)/ x + y < 2 } . d.Find f(x/y) where x = 1 and y =2.
Let us say that we have jointly distributed random variables X and Y with E(X) = 3,E(Y) = 5, Var (X) = 1, Var(Y) = 3, and Cov (X, Y) = 2.Determine:a) E(2X + Y) b) Var(6X)
(X³, 2Y²-3Y+4) Calculate the covariance by creating a common distribution table for the given random variables.