1.An office has four copying machines, and the random variable X measures how many of them are in useat a particular moment in time. Suppose that P(X = 0) = 0.08, P(X= 1) = 0.11, P(X= 2) = 0.27, andP(X = 3) = 0.33.What is P(X = 4)?Draw a line graph of the probability mass function.Construct and plot the cumulative distribution function.а.b.с.

Answered: An office has four copying machines,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Which of the following are a valid probability function for the given random variable? Select all that apply. 1 1 1 f(x) 1. O f(x) 1. 1. 1. 1. 2 O f(x) E) = 10 x = -1, –2, –3,-4 %3| O f(x) = x² + 1 x = 0.01, 0.02, . 0.99 ...* O f(x) = x 1 1 1 1. 2 3'6 ロf(@) x = 0,1,2, 3,4 10
The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. P(x, y) 1 2 0.015 0.010 0.025 1 0.030 0.020 0.050 2 0.075 0.050 0.125 3 0.090 0.060 0.150 0.060 0.040 0.100 0.030 0.020 0.050 What is the probability that there is exactly one car and exactly one bus during a cycle? What is the probability that there is at most one car and at most one bus during a cycle? What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = P(exactly one bus) = - Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflov during a cycle?
Assume that 1 out of every 5 adults in a local community is unemployed. Approximatethe probability that in a random sample of 100 adults from the community, more than 25are unemployed. Express your final answer in terms of the standard normal cumulativedistribution function Φ.
Exercise 3. Let X be a random variable with mean µ and variance o². For a € R, consider the expectation E((X − a)²). a) Write E((X - a)²) in terms of a, μ and σ². b) For which value a is E((X − a)²) minimal? c) For the value a from part (b), what is E((X − a)²)?
A random variable X has the following probability mass function for x = 0, 1, 2, 5. Based (PMF): P(X= x) = (x+1) 12 on this PMF, what is P(X≥ 2)? 5/12 1/2 3/4 11/12
QUESTION (3): A Factory produces packets of papers. The number of papers per packet varies as shown in the following table. NUMBER OF PAPERS 97 98 99 100 101 102 103 PROPORTION OF PACKETS .04 .13 .21 .29 .20 .10 .03 Draw the probability mass function (PMF). а. b. Calculate and draw the cumulative probability funetion (PDF). What is the probability that a randomly chosen packet will contain between 99 and 101 papers? с. d. Two packets are chosen at random. What is the probability that at least one of them contains at least 100 papers?
Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?
A shop receives a shipment of 1000 lamps. The probability that any individual lamp is defective is 0.2%. Assume the defectiveness is independent of cach lamp. Let X be the number of defective lamps in the batch of 1000. What is the probability mass function of X? O P(X = k) = (00) 0.002* (1 – 0.002)1000 , k = 0,1, 2, ..., 1000 O P(X = k) = 0.002* (1 – 0.002)1000–&, k = 0, 1, 2, .….., 1000 O P(X = k) = (1000) 0.002* (1 – 0.002)1000 , k = 1, 2, ..., 1000 O P(X = k) = (00)0.002100- (1 – 0.002)*, k = 0, 1, 2, ..., 1000
Find the probability P(Ec) if P(E)=0.17.

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