2. Given that X has the cumulative distribution function cdf 0 for x < -2 i for - 2< r < 0 I for 0 6 answer the following questions: (a) X is discrete or continuous RV? (b) The range set of X is? (c) Pr(X = 4) is? %3D (d) Pr(-1< X < 4) is? (e) Pr(X = 1) is?
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- If F(x) is the distribution function of X given by F ( x ) = 0 if x ≤ 1 k ( x − 1 )4 if 1 3 Colon noiludleb sdt Determine (i) f ( x ) (ii) kIn the conclusion of the Mean Value Theorem for the function f(x) = x, [0, 1] %3D 29 - Find the value or values of c that satisfy the equation f(b) - f(a) b- a f'(c) %3D O A) 5 O B) 9/33 C) 8/27 O D) 6/33 O E) 5/27The error involved in making a certain measurement is a continuous rv X with the following pdf. f(x) = {0.09375(4 -x²) -2≤x≤2 otherwise (a) Sketch the graph of f(x). f(x) 0.6 0.5 0.4 L 0.3 0.2 0.1 1 -2 -2 (b) Compute P(X > 0). f(x) 0.6 0.5 0.4 0.3 0.2 0.1 1 2 2 3 3 X X 0-3 -2 (c) Compute P(-1 1.1). (Round your answer to four decimal places.) -1 -1 f(x) 0.6 0.5 0.4 0.3 0.2 0.1 f(x) 0.6 0.5 0.4 0.3 0.2 0.1 1 1 2 2 3 3
- P(X = 5) = f(5) O for only continuous distributions. O for all distributions. O for some discrete distributions but not all. for only discrete distributions.2. A random variable X has a p.d.f. f(x) given by √(1-x)6 011 Assume the GPAS of high school students, X, follows a continuous uniform on the domain 1The cumulative distribution function F(x), for f(x) = =. 35 x<5 1s O a. x/8 O b. None of these O c. 1 O d. 0Which of the following best describes P(X < c) as it relates to the cumulative distribution function (cdf), F(x)? It is the total area under F(x). It is the area under F(x) to the left of c. It is the area under F(x) to the right of c. It is the value of F(x) at c. It is the area under F(x) at c.2. Determine whether each of the following distributions are exponential family. For those that are, find a set of complete, minimum sufficient statistics. For those that are not, find a sufficient statistic. (a) Location Exponential: f(x) = e-(-0), x > 0. (b) f(x) = 0(1+x)(1+0), x > 0 (c) logN(u,02): f(x) = 1 a exp{-(log x-μ)²), x > 0. αν2πσ2 },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 ≤ Ta X and Y are continuous variates. The conditional p.d.f. of X given Y = y is Yé for 0 < x < ∞o and 0 < y < ∞0. fi(x|y)= x + y 1+ y The marginal p.d.f. of Y is X f₂(y) = (1+y)e-y Find the marginal p.d.f. of X. for 0 < y < ∞o. CamScannerLet X represent the lifetime of a component, in weeks. Let Y represent the lifetime of the component in days, so Y = 7X. Suppose X ~ Exp(1). Let Fy be the cumulative distribution function of Y and let Fy be the cumulative distribution function of X. Show that Fy(y) = 1 e¯e-Ày/7. [Hint: F,(y) = P(Y < y) = P(7XSEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON