Problems1. Two discrete random variables X and Y have joint pmf given by the followingtable:Y31.1126.12116.41211.0.1212Compute the probability of each of the following events:(a) X <1.(b) X is odd.(c) XY is even.(d) Y is odd given that X is odd.2. Each telephone call passes through a number of switching offices before reachingits destination. The number and types of switching offices in the United Statesin 1971 were estimated to be as follows:i3.Office type Step-by-stepPanelCrossbarESS 1Number86005005700286"Electronic Switching System1.2.

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Answered: 1. Two discrete random variables X and…

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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Suppose X is a random variable with possible values -2, 4, and 2, and with respective probabilities 0.28, 0.48, and 0.24. Then E(5X-2 x2) is: O a. 2.4288 Ob.-10.32 Oc. 22.7424 Od. 15.9712 O e.-4.3424 Ne ch DELL
e. 1.773 15. Find the expected valuser a random variable having the following probability distribution: -1 1 -3 0 3/10 1/5 1/14 1/7 |is| + C. d. 33 70 19 35 109 140 33 140 P(X-x) 5 2/7
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Q P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5
3. 01:26:35 The following two-way table shows the distribution of daily traffic and weather issues in a certain large city. Suppose a day from this city is selected at random. Let event A = heavy traffic and event B = bad weather. Are events A and B independent? Daily Traffic No, P(A) = P(B|A). Нeavy Traffic Light Traffic Total O No, P(A) + P(A|B). O Yes, P(A) = P(A|B). O Yes, P(A) + P(B|A). Bad Weather 25 30 Good Weather 55 15 75 Total 80 20 100 Weather Conditions
Determine which of these statements is correct/incorrect and explain the reason why. a. X is a discrete random variable. Therefore, P(9 < X < 11) = P(X=9) + P(X=10) + P(X=11) b. The probability of flipping two coins will result in one head and one tail is 1/2 c. K and L are mutually exclusive events. P(K)=0.3 and P(L)=0.4. Hence, P(K∩L) = 0.12 d. There are mass points that have a probability of zero. That is, if x is a mass point, then it's possible that P(X=x) = zero.
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2 A random sample of size 12 drawn from a population of size 200. The sample values and their probabilities are (52,0.004), (72,0.003), (64,0.005), (58,0.003), (42,0.002), (76,0.006), (71,0.006), (63,0.006), (87,0.008), (57,0.002), (61,0.003) and (86,0.007). Estimate population total with a 95% confidence interval by using probability proportional to size sampling.
QUIZ (1/2 CW). Let X be a discrete random variable and S = {1,2,3,4,5,6,7} be its support. With the pmf of X given below, If xɛs Compute the f (x)={28 expected If x S value.
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1. Two discrete random variables X and Y have joint pmf given by the following table: 1 3. 1. 1. 12 6. 12 4. 12 3. 0. 12 12 Compute the probability of each of the following events: (a) X<1. (b) X is odd. (c) XY is even.