Problem 3.2: Let the p.d.f. of the continuous random variable X be the expression below. Compute: (c) E3-2X] (e) σχ (a) c (b) E[X] (d) Var(X) Jesin(Tr) for 0 < r ≤0.694 f(x) = elsewhere
Q: (37) Let X be a random variable with p.d.f. (x+1)e2* x=1,2,3 f(x) =- , find (1) k (2) E(x² +1) O.w
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Q: Let X be a random variable with p.d.f. x = 1,2,3 f(x) = { find (1) k (2) E(x²) O.W
A: Solution: 36. From the given information, the probability density function of X is
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Q: Let X be a random variable with p.d.f. {(k + 1)e¬8: f(x) = 0<x<0 , find (1) k (2) P(x< 1) O.w
A: Solution: 39. From the given information, the probability density function of X is
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Q: 16 a) A random variable has pdf £x (x) = ² (1-x²) fx 4 0 (1-x²) 0≤x≤1 Find E (4x+2) and E(x²). else…
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Q: (41) Let X be a random variable with p.d.f. [(k+4) 0<x<5 ,find (1) k (2) E(x +1) (x) O.w
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Q: Let X be a finite random variable on (N, F, P) (i.e., P(X = ∞) = P(X = -x) = 0). Show that its…
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Q: (24) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) =- , find E(e³*) O.w
A: Here,Ee5x=∫0∞e5xfxdx=∫0∞e5x2e-2xdx=2∫0∞e3xdx=2e3x30∞=23e3x0∞=23e3∞-e30=23∞-1=∞
Q: (7) Let X be a random variable with p.d.f. 1<x<0 f(x) = { ,find k. O.W
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Q: (36) Let X be a random variable with p.d.f. xe2k x=1,2,3 f(x)= , find (1) k (2) E(x²) O.w
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Q: (34) Let X be a random variable with p.d.f. x= 1,2,3 f(x) ={ , find (1) k (2) E(²) O.w
A: X is a random variable with pdf: The sum is always 1. So,
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- Suppose the random variable X has pdf K exp £x(u) = 2√/27 x ( - (a - 2²). - where A is a constant to be determined. Determine K, the CDF Fy, and the mean E[X]. 0 ≤ ≤ 4, otherwise.(22) Let X be a random variable with p.d.f. 3k e 04. Suppose X₁ and X₂ are independent random variables with cdf Fx(x) = sin(x), 0 ≤ x ≤ 1/ a. Show that fx(2) (x) = 2sin(x) cos(x), where X (2) is the random variable for the 2nd order statistic. (Remember, we only have 2 random variables.) b. Show that fx(1)(x) = 2cos(r) [1 sin(x)], where X(1) is the random variable for the 1st order statistic.Let X1, X2, ..., Xn be a random sample from a normal distribution with mean u and variance o?. Find an unbiased estimator for o? and show that ΣΧ-Χ- E(X; - X)² = E(X²) – nX². i=1 i=1(35) Let X be a random variable with p.d.f. 2k x=1,2,3 f(x) = { find (1) k (2) E(x+1) O.w(54) Let X be a random variable with p.d.f. [(k+4) f(x) = { 18. Let the random variable X have the pdf 2 x2 fx (x) = exp %3D - V2n 2 Find the mean and the variance of X. Hint: Compute E (X) directly and E (X²) by comparing the integral with the integral representing the variance of a random variable that is N(0,1). i DCO 04 < (X - 5)2 < 38.4).(11) Let X be a random variable with p.d.f. k 14. Using the inverse CDF method, find formulae for generating random variables having the following PDFs: (a) f(x) = 2 cos x 3 sin³ x " (b) f(x) = 8x (x + 1)³ 0≤x≤1. 3"Recommended 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,