Problem 2.3: A continuous probability distribution is expressed through the following expression. Find: (a) c, (b) P(0.1 < X < 1.8), (c) F(X) Sce-8r for a 2 0 f(r) = elsewhere Problem 2.4: A joint discrete probability function f(x, y) is expressed in the table below. Find: (а) с (b) P(1 < X < 3, 1.5 < Y < 1.7) (c) P(2.5 < X < 3.5) (d) P((X +Y) < 4.6) (e) the marginal distributions fx(x) and fy(y) (f) whether the random variables X and Y are statistically independent. f(x, y) 2.1 3.7 2.9 1.56 0.01 0.05 0.07 y 1.64 0.04 1.72 0.21 0.17 0.02 0.03 Problem 2.5: A discrete joint probability distribution is expressed through the expression below. Find: (a) c (b) P(2 < X < 6, 3 < Y < 5) (c) P(2.5 < X < 18.5) (d) P((X +Y) > 7) (e) the marginal distributions fx(x) and fy(y) 1 for r = 2, 5, 10, y = 2, 4, 5, where (X +Y) > 4 xy f(x, y) = for r = y = 2 C elsewhere

Problem 2.3: A continuous probability distribution is expressed through the following expression. Find: (a) c, (b) P(0.1 < X < 1.8), (c) F(X) Sce-8r for a 2 0 f(r) = elsewhere Problem 2.4: A joint discrete probability function f(x, y) is expressed in the table below. Find: (а) с (b) P(1 < X < 3, 1.5 < Y < 1.7) (c) P(2.5 < X < 3.5) (d) P((X +Y) < 4.6) (e) the marginal distributions fx(x) and fy(y) (f) whether the random variables X and Y are statistically independent. f(x, y) 2.1 3.7 2.9 1.56 0.01 0.05 0.07 y 1.64 0.04 1.72 0.21 0.17 0.02 0.03 Problem 2.5: A discrete joint probability distribution is expressed through the expression below. Find: (a) c (b) P(2 < X < 6, 3 < Y < 5) (c) P(2.5 < X < 18.5) (d) P((X +Y) > 7) (e) the marginal distributions fx(x) and fy(y) 1 for r = 2, 5, 10, y = 2, 4, 5, where (X +Y) > 4 xy f(x, y) = for r = y = 2 C elsewhere

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.4: Total Differentials And Approximations

Problem 23E: Eastern Hemlock Ring shake, which is the separation of the wood between growth rings, is a serious...

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