13. The loss random variable X has a probability generating function 1 P(z) = = 2-z What is E[XA 3]?
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![13. The loss random variable X has a probability generating function
1
P(z) =
=
2-z
What is E[XA 3]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4732789b-cd00-49f2-995b-b63df0176a48%2F73693e8e-485f-4d4a-bc76-6c8a1a2e8b42%2Fxhxqepo_processed.png&w=3840&q=75)
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- The cumulative distribution function of random variable Y is given by y < 0 Fy(y) : 0 < y < b b < y where b = 0.125. Random variable W is a transformation of Y such that W = 15Y. What is the probability that W is less than 5, that is, P(W < 5)?(32) Let X be a random variable with p.d.f. e2k x= 1,2,3 (x-1)! f(x) = , find (1) k (2) E(2x) O.w7. A discrete random variable X taking non-negative integer values has probability gen- erating function: 1 rx(t) = (2- t)2 (a) Calculate P(X = 2).
- (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.w3. Let X1, and E- X; are independent. , Xn be iid with exponential distribution with mean 0. Show that (X1+X2)/ E=1 X;der a random sample X1, X2, ..., X, having the pdf, f(r; 0) 12. A random variable X has a p.d.f. f(x) given by √(1-x)6 0Which of the following is false for continuous and independent random variables Y and Z?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))³3. Suppose X is a discrete random variable with pmf defined as p(x) = log10 ( for %3D x = {1,2,3,...9} Prove that p(x) is a legitimate pmf.1. Verify whether the following functions can be considered as probability mass functions: (i) P(x = x) = x² + 1 18 (iii) P(X= x) = -, x = 0, 1, 2, 3 (ii) P(X - x) - ²-2, -, x= 1, 2, 3 2x + 1 18 -, x = 0, 1, 2, 3 [Ans.: Yes) [Ans.: No] [Ans.: No]Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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