X = the number of occurrences of a particular event in an interval of time or space.2x. e-2P(X = x) =X = 0, 1, 2, 3, ....%3Dх!Е(X) - 7,Var(X) = ..Table III (pp. 580 – 582)givesP(X< x)1.Traffic accidents at a particular intersection follow Poisson distribution withan average rate of 1.4perweek.a)What is the probability that the next week is accident-free?b)What is the probability that there will be exactly 3 accidents next week?c)What is the probability that there will be at most 2 accidents next week?

Answered: Image /qna-images/answer/c0964fdd-274d-493a-b5fb-a604f6016697.jpg

Answered: X = the number of occurrences of a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A Example 17-50. Obtain 100 (1 – a)% confidence limits (for large samples) for the parameter 1 of the Poisson distribution : e-^ . 2* f(x, 1) = -;x = 0,1, 2,... x !
Q. 2 Suppose I see students during regular office hours. Time spent with students follow an exponential distribution with mean of 20 minutes. (i) Write the probability density function of random variable X, E (X) and Var(X). (ii) Find the probability that a given student spends less than 0.4 hours with the professor. (iii) Find the probability that a given student spends between 0.20 and 0.5 hours with the professor. (iv) Find the probability that a given student spends at least 0.75 hours with the professor.
Which of the following is a valid cumulative distribution function? Note: the arrow means the line extends to +inf.
ANSWER COMPLETELY FOR UPVOTE
Find the standard deviation. Р(x) | x*Р(x) (x - 4)°P(x) 2 0.1 2(0.1) = 0.2 4 0.3 4(0.3) = 1.2 6 0.4 6(0.4) = 2.4 8 0.2 8(0.2) = 1.6 00
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 },
7. Prove or disprove that the following function is a cumulative distribution function (cdf). If the function is a cdf, is the random variable continuous or discrete? Why? (Note: This is a special case of a logistic distribution.) Fx(x)= 1 1+ e-z -∞<<∞.
min {X1, X2}. %3D Suppose that X1, X2 are iid, and X1 Exp(2). Find the distribution of X(1)
Number of 0 1 2 3 4 5 6 malfunctions: Probability: f(x) | 0.17 0.29 0.27 0.16 0.07 0.03 0.01
6b
Q.7 For an exponential distribution fx(x; p) = (ue H, x20 %3D e. w. where u > 0 Write (Don't derive) (a) Mean (expected value), i.e. E(X). (b) Standard deviation, i.e. S.D. (X). (c) Moment generating function, i.e. Mx(t). (d) Cumulative distribution function (cdf), Fx(x). of Nizv
3. (20%) Let W1 < W2 < W3 < W4 < W5 < W6 be the order statistics of n = 6 independent observations from f(x) = x/2; 0 < x < 2. (a) Find E(W6)

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