7. Suppose that S = {1,2,...n+1} where n ≥ 2. Let T = {(z. y, z) | r.y. z € S.r
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- 10. The interval for |(z )/5-1|<1 is Oa. [0,10] Ob. (0,10) Oc. (0,2 ) Od. [0,2 ]Show that if X ∼ Geom (p) then P(X = n + k | X > n) = P(X=k) for n, k≥1.5. Let f(x, y) = P(X =x,Y = y), X = 2,3,4, Y = 1,2,3,4, where P is given by the table below: X = 2 X = 3 X = 4 Y = 1 Y = 2 Y = 3 1/20 2/20 1/20 2/20 1/20 3/20 1/20 2/20 2/20 2/20 1/20 Y = 4 2/20 For problems (a) - (d) below write your work using the correct notation in terms of f (e.g. f(x, y), fy: f,(3), fyp fxp(4) ): (a) Verify that f is a joint probability mass function. (b) Find the marginal distribution for each random variable. Are both random variables independent? (c) Find the mean and variance of each marginal distribution. (d) Find the conditional probability function of Y given X =3. (e) Find E(Y|X = 3) and V(Y|X = 3). (f) Find P(X+Y =5), P(Y >1), and P(X +Y =5|Y > 1).
- 6. Evaluate 1 2 + 2 + 22 E ; dV, where E = { (r, y, z) | 1 < x2 + y2 + 22 < 4 }. =4.08 Consider Y with pmf p(y) = exp(-3.8)(3.8)'-2/(y-2)! defined on some set. ( a Determine a valid set. ( b Calculate P(Y > 3).X. 30. Which of the following sets are equal? A = {x e R-2Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,