Q1 Let X be a non-negative discrete random variable. Prove that the expected value of X satisfies E(X) = [ +∞o (1 - F(x)) dx
Q: satisfies F(-1) = 0.25, F(0) = 0.33, F(0.8) = 0.72, F(3.2) = 0.72, F(9.9) = 1. Find the value of…
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Q: (34) Let X be a random variable with p.d.f. 1<x<» k f(x) = { find k. O.w
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Q: 3) Let X be a continuous random variable with PDF x20 fx(x) ={0 otherwise Find E[X], Var[X] and M…
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A: ANSWER: Form the given data,
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A: the selection of a point in the closed interval [0,2a] is a uniform random variable X.
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Q: A random variable X has the pdf as f(x) = ax + b, for 0 < x< 1. The mean of X is E(X) = 2/3. (1)…
A: Given,f(x)=ax+b ; 0≤x≤1E(X)=23
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Q: Consider a continuous random variable X with the pdf 0 < x < 1 f(x) = { J x, | c/x³, 1<x <∞ Find (a)…
A: The PDF is a probability that a random variable, say X, will take a value exactly equal to x.
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A: From the provided information, Mean (λ) = 2 X~exp(2)
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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…
Q: 5. Let X be a random variable with the PDF f(x) = r - 1| for 0 0.5) (c) Calculate E(X) and Var(X)
A: The pdf of X is
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Q: A random variable X has a pdf [c(1-x*) -1<x <1 fx(x) otherwise (i) Find C. (ii) Find P[|x|<1/2].
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Q: Let X be a continuous random variable with pdf f(x) = x² for -1 < x < c. Find the value of c.
A: From the given information, the pdf of the random variable X is,
Q: (21) Let X b (12,5) find E(5+6x) and distribution function.
A: Given,X≈b(12,23 )E(x)=npE(x)=12×23 E(x)=8
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- The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp (-x/3100)]/3100 for x > 0 and f (x) = 0 for x ≤ 0. Determine the probability that:(a) A component lasts more than 1180 hours before failure.(b) A component fails in the interval from 1180 to 2010 hours.(c) A component fails before 3010 hours.(d) Determine the number of hours at which 11% of all components have failed.(e) Determine the mean.Round your answers to three decimal places (e.g. 98.765).Show that for any random variable E[X2]≥ (E[X])² and When does one have equality?f(x)= k(3x+4), x = -1,0,1,2 Find expected value E(X) . Select one: O a. 0.5 O b. 1 O c. 1.182 с. O d. 1.5
- Suppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤ TThe diameter of a round rock in a bucket, can be messured in mm and considered a random variable X in f(x) f(x) = k(x-x4) if 0 ≤ x ≤ 1f(x) = 0 otherwise. Find the expectation E(4X+ 3) and variance V(4X+3)Let X1, X2, ..., Xn be a sequence of independent and identically distributed random variables having the Exponential(A) distribution, A > 0, de-dr ,r >0 fx,(x) = { 0 , otherwise (a) s< A; Show that the moment generating function mx(s) := E(e®X) = , for (b) Using (a) find the expected value E(X;) and the variance Var(X;).4. Let X be a positive random variable (i.e. P(X 1/E(X) (b) E(-log(X)) > -log(E(X)) (c) E(log(1/X))> log(1/E(X)) (d) E(X³) > (E(X))³Suppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤ TIf E[X] = 1 and Var(X) = 5, use definition of variance and properties of expectation to find (a) E[(2 + X)^2] (b) V ar(aX) for any constant a. (c) V ar(X + b) for any constant b. (d) V ar(4 + 3X)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,