4. Suppose that X and Y are random variables having the joint probability distributiony13520.15 0.100.250.250.150.10Finda) Marginal distribution alone X and alone Yb) E(2X - 3Y);c) E(XY)d) Are X and Y independent random variables? If yes show

Given, X=2 X=4 Total Y=1 0.15 0.10 0.25 Y=3 0.25 0.25 0.5 Y=5 0.15 0.10 0.25 Total 0.55…

Answered: 4. Suppose that X and Y are random…

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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True False? a)A sided dice with the probability of 1 and 6 coming p and the other numbers (2, 3, 4, 5) is 2p is rolled n times. x̄, is the average of the numbers in n shots. According to this information, p = 2 / 5x̄. b)If X1, ..., Xn, N is a random sample drawn from the distribution (μ, ϭ²), the sample mean x̄ and sample variance S² are always independent.
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3. Table 1 below shows the probability distribution of hurricanes that have made landfall in the Caribbean. The random variable, X, is the category of the hurricane. Category 1 is the weakest hurricane level while category 5 is the strongest. Table 1 x 1 2 3 4 5 P(X=x) 0.41 0.34 0.13 0.07 * a) Find the value of ‘*’. [1] b) Find the expected category of hurricane to make landfall, E(X). [2] c) What is the probability that a Category 4 or stronger hurricane will make landfall?[1] d) Calculate the variance. [3]

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4. Suppose that X and Y are random variables having the joint probability distribution Y 2 1 - 3 5 0.15 0.25 0.15 I 0.10 0.25 0.10 Find a) Marginal distribution alone X and alone Y b) E(2X 3Y); c) E(XY) d) Are X and Y independent random variables? If yes show