1. Suppose that X and Y have the following joint probability distributionY1210.050.050.120.050.10.3530.20.1A. Evaluate the marginal distribution of XB. Evaluate the marginal distribution of YC. P (x= 2) & P(y=2)D. The conditional distribution of Y given x=3E. The conditional distribution of X given Y=1F. P( x=1/ y=2)G. Determine if the two random variables are statistically dependent or independent2. A privately owned liquor store operates a drive up facility and a walk-in facility. On a randomly selected day, letX and Y, respectively be the proportions of the time that the drive-up and walk-in facilities are in use andsuppose that the joint density function of these random variables is given by(х + 2y),0< x<1,0 < y<1fx =elsewhereFind PG < x < & y <а.b. Find the marginal density of XС.Find the marginal density of Yd. Find the probability that the drive-up facility is busy less than one-half of the timeе.Find the probability that the walk-in facility is used more than two-thirds of the timey2f.Find P(

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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12. i. State Central limit theorem and tell what is the main theme of it. ii. Show that if the random variables (X, Y) follow the probability density of a bivariate normal distribution and if the correlation p = 0, X and Y are independent. (Show that f(x, y) = g(x) h(y))
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Assume that daily evaporation rates (E) have a uniform distribution with a = 0 and b = 0.35 inches/day. Determine the following probabilities:Pr (E ≥0.1) Pr (E ≤ 0.22) Pr (E = 0.2) Pr (0.05 ≤ E ≤ 0.15

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1. Suppose that X and Y have the following joint probability distribution Y 1 2 3 1 0.05 0.05 0.1 0.05 0.1 0.35 3 0.2 0.1 A. Evaluate the marginal distribution of X B. Evaluate the marginal distribution of Y C. P (x= 2) & P(y=2)