11. A continuous random variable X has a probability density function f, where A(1 – 2²) S(z) = clsewhere " The cumulative probability function F(z) = 0, z<0 A A(1 - ), z>1 A(z - ), B |0, 15= > 0 elsewhere 0, A(z - 4). 1, z< 0 z>1 [0, (z - 4), 0, I<0 D 0, I>1
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- 5 Suppose the distribution function of the continuous random variable { is 1-es*, x20; F(x)=• 0, x3); (2) the density function f(x)9 Let the probability density of the two-dimensional random variable (ξ, η) be (4e**, x > 0; f;(x)=• (0, 6e", y>0; -6y f,(v) =; 0, x<0. y<0. Find E(2 { +3 n ).3. The probability density functions of two statistically independent random variables X and Y are fx(x) = }u(x - 1)e-lx-1)/2 fr(y) =u(y- 3)e-(s-3)/4 %3D Find the probability density of the sum W =X+Y.
- Q5 Let = {} 1 f(x) = x = 1, 2, 3, 4, 5, 6, otherwise. be the probability mass function of a discrete random variable X. Show that the probability mass function of the smallest observation Y₁ of a random sample of size 5 from this distribution is 5 91 (y₁) = = (²-")" - (0 =³) "₁ 6 6 y = 1, 2, 3, 4, 5, 6. and zero otherwise. Note: you already know how to write down the cumulative distribution function of Y₁, the smallest of X₁, X₂, X3, X₁, and X5; remembering that we are sampling from a discrete distribution, derive the probability mass function of Y₁.7نقطتان )2) Q10) If you know that is the following function is joint probability density function, * ?what is the value of t S9xy 0Recommended 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,