4. (Sec. 5.3) There are two traffic lights on a commuter's route to and from work. Let X1 be the numberof lights at which the commuter must stop on his way to work, and X2 be the number of lights at whichhe must stop when returning from work. Suppose these two variables are independent and identicallydistributed, each with pmf given in the table below (so X1 and X2 are a random sample of size n = 2).01 2P(x) .3 .5 .2Note that u = 0.9 and o² = .49.(a) Determine the exact pmf of the total number of stops at traffic lights during the commute,To = X1 + X2.(b) Calculate µT, - How does it relate to µ, the population mean?(c) Calculate o. How does it relate to o², the population variance?(d) Let X3 and X, be the number of lights at which a stop is required when driving to and from workon a second day, assumed independent of the first day. With To =the sum of all four X;'s, whatnow are the values of E[T,] and V[To]?

Name: 4. (Sec. 5.3) There are two traffic lights on a commuter's route to a
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 4. (Sec. 5.3) There are two traffic lights on a commuter's route to and from work. Let X1 be the numberof lights at which the commuter must stop on his way to work, and X2 be the number of lights at whichhe must stop when returning from work. Suppos

Consider the given table of probability marginal function for two independent and identically…

Math

Advanced Math

of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose these two variables are independent and identically distributed, each with pmf given in the table below (so X1 and X2 are a random sample of size n= 2). |0|1|2 P(x) | .3 .5 2 Note that µ = 0.9 and o² = .49. (a) Determine the exact pmf of the total number of stops at traffic lights during the commute, To = X1 + X2.

of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose these two variables are independent and identically distributed, each with pmf given in the table below (so X1 and X2 are a random sample of size n= 2). |0|1|2 P(x) | .3 .5 2 Note that µ = 0.9 and o² = .49. (a) Determine the exact pmf of the total number of stops at traffic lights during the commute, To = X1 + X2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

n 5.6.4. Show that ô² = ΣY? is sufficient for o² if i=1 Y1, Y2,..., Yn is a random sample from a normal pdf with μ = 0.
1. The proportion of rats that successfully complete a designed experiment (e.g., running through a maze) is of interest for psychologists. Denote by Y the proportion of rats that complete the experiment, and suppose that the experiment is replicated in 10 different rooms. Assume that Y₁, Y2,..., Y₁o are i.i.d. Beta random variables with a = 2 and 3 = 1. Recall that for this Beta model, the pdf is (2y if 0 0.9). otherwise.
1.9.18. Find the mean and the variance of the distribution that has the cdf x <0 0
6.2.2 If (x₁, ..., xn) is a sample from a Bernoulli(0) distribution, where 0 = [0, 1] is unknown, then determine the MLE of 0. 6.2.3 If (x₁,...,xn) is a sample from a Bernoulli(0) distribution, where 0 = [0, 1] is unknown, then determine the MLE of 0².
= Suppose X is normally distributed with a mean of u 10 and a variance of o² = 9. Further suppose that a random sample of n = 50 has been taken from this population. Which of the following statements is/are true about the distribution of the associated sample mean, X? Select one or more: U a. The distribution of X will be Normal b. The distribution of X will have a variance of 3 □ c. The distribution of X will have a variance of greater than 9 The distribution of X will have a variance of g 50 O d. O.e. The distribution of X will be unknown Of. Og. 9 The distribution of X will have a standard deviation of 50 9 The distribution of X will have a standard deviation of √50
3. An individual who has automobile insurance from a certain company is ran- domly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is 1 p(y) | .60 .25 .10 .05 What is the variance of Y? Α. 1.1 В. .60 C. .79 D. 1 E. None of the above 4. Based on the pmf in problem 3, what is the probability that an individual was cited between 1 and 3 times (inclusive)? A. .25 В. .05 С. .30 D. .40 E. None of the above
llustration 19.18.. A sample study of the population of two districts gives that in district A the percentage of male population is 52% while this is the figure for the female percentage in the B district. If the size of the sample selected was in district A and B as 400 and 625 respectively, can both of these samples be taken to come from a population where the percentage of males and females is equal?
3.3.24. Let X1, X2 be two independent random variables having gamma distribu- tions with parameters a₁ = 3, B₁ = 3 and a2 = 5, B2 = 1, respectively. (a) Find the mgf of Y = 2X₁ +6X2. (b) What is the distribution of Y?
Let X-1: correct, X=0 : wrong And P= Pr(X=1)=2/5 What is the variance? .32 O.6 O .4
. In a trivariate distribution. o, = 3, o, = 4, o, = 5 rn = 0.4, r, = 0.6 r,, = 0.7 Determine the regression equation of X. on X, and X, if the variates are measured frem their means.
24
5