From a sack of fruit containing 3 apples, 2 bananas, and 3 oranges, a random sample of 4 pieces of fruit is selected. Suppose X is the number of apples and Y is thenumber of bananas 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+ys 1}.(a) Complete the joint probability distribution below.(Type integers or simplified fractions.)f(x,y)134y1234(b) The probability is(Type an integer or a simplified fraction.)

Answered: From a sack of fruit containing 3…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1. Let X1, X,.., X, random sample from distribution be a a Geometric 2....., fx (x) = p(1– p)*| F, (y,) = ? x-1 x=1,2,3,.... Fy, (y,) = ? P(Y, <1) =? а. b. С.
9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: (f(x|y = 1)
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Let X; (i = 1, 2,..., n) be i.i.d. exponential random variables with E{X;} = 1/A. Let Y = mn{X1, X2,..., Xn}. What is the distribution of Y? (Compute P{Y > y}.) What is the distribution of Z = max{X1, X2, ..., Xn}? (Compute P{Z < z}.)
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D5) X and Y are two points that are selected according to a uniform distribution. Calculate the expected value of the distance between these two points for each of the following cases: a) Both X and Y are selected independently from the range 0-1. b) We select X between 0 and 1 and then select Y between 0 and X. Note: For case b the distance is equal to |Y-X|
Let X and Y denote the weights (in grams) of apples which are imported from two different locations: Peshawar (Pakistan) and Zanzibar (Tanzania), respectively. Suppose that X has Normal distribution N(148, 3); and Y has Normal distribution N(151, 4). One apple is randomly selected from each city. We assume independence between X and Y. • [[a)] Find the probability that the weight of the apple from Peshawar exceeds the weight of the one from Zanzibar • [(b)]A random sample of 36 apples is selected from those imported from Peshawar. Compute the probability that their sample mean will fall between 150 and 152. Paragraph BI Path: p pe here to search II !!!
(a). Derive the theorem of total chance of occurrence of engineering events. (b). If Faculty of Engineering and Technology is located south of the land of Malete and experiences Wet and Dry seasons yearly. Assume the Wet season in the vicinity of the building lasts for 1/3 of the year, and the Dry season for 2/3 of the year. The chances of rain falling during the wet and dry seasons are 3/4 and 1/6, respectively. i. If you visit the engineering building on a random day of the year, what is the chance that it will rain on arrival? If you visit the engineering building on a random day, and it rains on arrival. What is the chance that your visit is during the wet season? ii.
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