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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Answered: 1. Suppose that X and Y have the…

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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7. Assume that X and Y have a bivariate normal distribution having means 14.l and 1.3, and standard deviations 2.5 and 0.1, respectively, with correlation coefficient 0.8. Find P(Y >1.4|X =15) and P(X >15|Y = 1.4).
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You take a simple random sample of size 25 from a very large population in which the true proportioni p=0.1. Which statement below best describes what you know about the sampling distribution of p? (0.1)(0.9) (a) H,-0.1; o,- the distribution is skewed right. 25 (0.1)(0.9). 25 (b) H,=0.1; o,=. ; the distribution is skewed left. (0.1)(0.9). (c) ,=0.1; o,= the distribution is approximately Normal. %3D 25 (0.1)(0.9) (d) , the distribution is not approximately Normal. 25 =0.1; we cannot use the formula o, (0.1)(0.9) ; the distribution is approximately Normal. 25 (e) =0.1; we cannot use the formula o,
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)