There are two traffic lights on a commuter’s route to and from work. Let \( X_1 \) be the number of lights at which the commuter must stop on his way to work, and \( X_2 \) be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so \( X_1, X_2 \) is a random sample of size \( n = 2 \)).\[\begin{array}{c|ccc}x_1 & 0 & 1 & 2 \\\hlinep(x_1) & 0.1 & 0.3 & 0.6 \\\end{array}\]\[\mu = 1.5, \quad \sigma^2 = 0.45\](a) Determine the pmf of \( T_0 = X_1 + X_2 \):\[\begin{array}{c|ccccc}t_0 & 0 & 1 & 2 & 3 & 4 \\\hlinep(t_0) & & & & & \\\end{array}\](b) Calculate \( \mu_{T_0} \):\[\mu_{T_0} = \underline{\hspace{1cm}}\]How does it relate to \( \mu \), the population mean?\[\mu_{T_0} = \underline{\hspace{1cm}} \cdot \mu\](c) Calculate \( \sigma^2_{T_0} \):\[\sigma^2_{T_0} = \underline{\hspace{1cm}}\]How does it relate to \( \sigma^2 \), the population variance?\[\sigma^2_{T_0} = \underline{\hspace{1cm}} \cdot \sigma^2\]

Given X 1 0 1 2 P(X1) 0.1 0.3 0.6

Answered: There are two traffic lights on 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...

See similar textbooks

Similar questions

According to the Max Markwell classifica- tion, there are three types of drivers on High- way 71 between Bastrop, Texas and Austin, Texas: Good, Bad, and Egregious. 12% of all drivers are Good ●68% of all drivers are Bad • All remaining drivers are Egregious Good drivers drive in the passing lane 28% of the time (e.g., only while actively passing or making a left turn within the next 1/2 mile) • Bad drivers drive in the passing lane 74% of the time Egregious drivers camp in the passing lane 100% of the time. You observe a driver in the passing lane. De- termine the probability that the driver is a Bad or Egregious driver. NOTE: Round to the nearest whole percent. Answer in units of percent.
A research study was conducted about gender differences in 'sexting'. The researcher believed that the proportion of girls involved in 'sexting' is different from the proportion of boys involved. The data collected in the spring of among a random sample of middle and high school students in a large school district in is summarized next: out of 380 females 43 sent 'sexts' and out of 410 males 64 sent 'sexts'. Is the proportion of girls sending sexts different from the proportion of boys 'sexting'? Choose the appropriate procedure. Procedure: Assumptions: (select everything that applies) Population standard deviations are known Normal populations Sample sizes are both greater than 30 Population standard deviation are unknown but assumed equal Paired samples Population standard deviation are unknown Simple random samples The number of positive and negative responses are both greater than 10 for both samples Independent samples
At the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also random with an average rate of 22 vehicles per minute. If the operator of the toll road in the previous problem wants to improve the current condition at the toll plaza, determine the new queue characteristics if the number of toll booths is increased to 2. Estimate average length of queue formed at the toll gate O 0.54 O 0.24 O 0.44 O 0.34
Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).
Two random variables X andY are related by the expression Y = aX +b, where ta' and 'b' are any real numbers.
Central Eye Clinic advertises that 90% of its patients approved for LASIK surgery to correct vision problems have successful surgeries. (b) Use the random digit assignment model of part (a) to simulate the outcomes of 15 trials. Begin at column 1, line 2. (Enter S for success and F for failure, separated by commas.)
Please don't provide handwritten solution .....
Consider a set of data points {(-10,13), (-6,9), (-6,17), (-2,13), (-3,0)}. Use the k-means clustering procedure with k = 2 to groups these data points. Start with the three initial cluster centers: (-6,9), (-2,13), (10,15). Show your working for 2 iterations. Use D= for distance calculation.
Suppose we want to test the hypothesis that mothers with low socioeconomic status (SES) deliver babies whose birth weights are different from normal. To test this hypothesis, a random sample of 100 birth weights is selected from a list of full-term babies of SES mothers. The mean birth weight is found to be 115 oz. Suppose the average birth weight of all babies (based on nationwide surveys of millions of deliveries) is known to be 120 oz with = 24 oz. Set = .05 Assume all conditions are met, what is the p-value of their test? Give your answer to 4 decimal places.
Matias is a student of standard 10 in St. Xavier Int. School. He has to study 7 subjects. In the annual exam, the performance of a student in each subject is graded as “G” (good), “M” (moderate) or “B” (bad). If a student gets at least one B or more than 2 M’s or both, s/he can’t get a scholarship next year. If all three grades are equally likely for Matias, what is the probability that he gets a scholarship next year?
A coffee shop owner offers two brands of coffee, Brand "A" and Brand "B". The proportion of clients that prefer Brand "A" is 60%. Recently, the price of Brand "A" went up. The proportion of clients that buy brand "A" among the first 15 customers that enter the shop after the change in price is an estimator of the current proportion of clients that prefer Brand "A". Assume that the change in price has no effect on the preference of the clients. Then the mean squared error (MSE) of the estimator is equal to: (Give an answer of the form x.xxx, i.e. with 3 significance digits) (HINT: Carefully read the definition of MSE in Chapter 10 of the text book.)
The table below shows head length and breadth of siblings. The four variables are X₁ = head length of first son, X₂ = head breadth of first son, X3 = head length of second son, and X₁ = head breadth of second son obtained from 25 families. Do first and second sons differ in their average head dimensions? State appropriate null hypothesis for this and test at a = 0.05 and interpret results. You may use softwares for computations but make sure to give (X₁-X3) all necessary details. Hint: Define Y = and state Ho in terms of Y. (X₂-X₁) Table 1: Head dimension data from Frets (1921), measured on siblings in 25 families X₁ X₂ 191 155 195 149 181 183 176 208 189 197 188 192 186 179 195 202 194 163 195 186 181 175 192 174 176 197 190 148 153 144 157 150 159 152 150 161 147 153 160 154 137 155 153 145 140 154 143 139 167 153 X3 179 201 185 188 171 192 190 189 197 187 179 183 174 190 188 161 183 173 182 165 185 178 176 200 187 X4 145 152 149 149 142 152 149 152 159 151 158 147 150 159 151 130…

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS