The probability that a soldier in particular region will be infected by a particular type of hepatitis is 1/800. There are presently 5000 British soldiers in this region. Find (approximately) the probability that at most 10 of the British soldiers will be infected by this type of hepatitis. (Assume that a soldier can get infected independently of the other soldiers.) Use a Poisson approximation. 0.583 0.674 0.986 0.014 0.946
Q: QUESTION 15 It is known that 4% of the light bulbs produced by a certain factory have short life…
A: Given : p = 0.04 , 4% of the bulbs have short life span Here , n = 50 Let X denotes the number of…
Q: Suppose that the probability of a successful optical alignment in the assembly of an optical data…
A:
Q: A stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain, A, so…
A: Given that stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain,…
Q: Suppose X is a discrete random variable with finite first and second moments. Show that E (x…
A: It is given that X is a discrete random variable with finite first and second moment.
Q: A Gaussian random variable X with u, = 4 and o =3 is generated. Find the probability of X <775,…
A:
Q: Q: Suppose the time to failure (in years) for a particular component is distributed as an…
A: Solution
Q: 20% of the workers in a factory work in plant A and 80% work in plant B. The number workers…
A:
Q: Suppose that in a certain small town it either rains or is sunny every day. A meteorologist notes…
A: Given that the probability that it showers today=80%=0.80 So the probability that it is sunny today=…
Q: Suppose a die is tossed 1500 times and a 3 comes up 601 times. Find the empirical probability for a…
A: Solution-: Given: Suppose a die is tossed 1500 times and a 3 comes up 601 times. We want to find the…
Q: Three components are randomly sampled, one at a time, from a large lot. As each component is…
A: The objective of this question is to find the mean (μx) of the number of successes when three…
Q: A particular unfair coin is constructed so that the probability of obtaining a tail is 4/5. The…
A:
Q: 1) A random variable X is defined by: X = -2 3 1 Find the first four moments about the mean. prob.…
A: The question is about moments Given : To find : First 4 moments about the mean
Q: One way to measure the diversity of a population of organisms is to calculate its Gini-Simpson…
A: Here, p is the proportion of cells of red-type.
Q: A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white…
A: We have two random variables X and Y such that PYy=0 p0=121 p1=12 The conditional density…
Q: Suppose X is a random variable and suppose the possible values that it can assume are given by a, b,…
A: Given, X is a random variable
Q: The mean of a discrete random variable x. Select one: O a. is none of these b. is correctly…
A: The mean of a discrete random variable is customarily denoted by μ.
Q: A simple random sample of size 200 is taken from a much larger group of male wrestlers prior to a…
A: Given Information: Sample size n=200 Sample mean x¯=190 Standard deviation s=20 The average weight…
Q: Let Kx be the curtate future lifetime random variable, and 9x+k= 0.1(k+1), for k= 0, 1, ..., 9.…
A: Here the data is given that, qx+k = 0.1(k+1) for k=0,1,2,....,9.
Q: Example 5.3. An experiment on rabbits is designed by taking N = 20 identical rabbits. But rabbits…
A: Introduction :- Here we have to find an appropriate probability law means distribution for the…
Q: Section I 1. Consider a discrete random variable X with pmf summarized in the table below. -3 4.…
A: 1. The given probability mass function table is, x -3 2 4 fx 0.45 0.3 0.25
Q: Find the CDF of an exponential random variable with mean 1/λ .
A: Solution
Q: The probability that a particular species of a plant will germinate is 0.67. What is the probability…
A: Given that, Number of seeds is n=120 Probability that a particular species of a plant will germinate…
Q: that the tax return will have at least one computational error. Whether one tax return has a…
A: Hello. Since your question has multiple parts, we will solve first 3sub parts question for you. If…
Q: öad nétwörk pictured in Figure 4.8.1. The inputs are Poisson processes with the rates indicated, and…
A:
Q: Question 12 A maintenance fırm has gathered the following information regarding the failure…
A: Given: Gas leaks Yes Gas leaks No Total Electrical failure Yes 55 17 72 Electrical failure…
Q: X̄ be the mean of a random sample drawn form a population with a mean μ and variance σ2 =9 . Find…
A: Confidence interval: It is defined as the range that contains the value of the true population…
Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…
A: We have given that X is a continuous random variable that takes on values between 10 and 40, then…
Q: A certain system is based on two indeperndent modules, A and B. A failure of any one of these…
A: Given: Modules A and B are independent modules. λA=0.1λB=0.25 X≥12 The pdf of an exponential…
Q: x1: New England Crime Rate 3.3 3.7 4.0 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 =…
A: Given that, x1: New England Crime Rate 3.3 3.7 4.0 3.9 3.3 4.1 1.8 4.8 2.9…
Q: 7% of messages on Jmes.com have objectionable material. This means that if we randomly select a…
A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…
Q: Suppose X and Y are random variables with E[Y]X] = -x +3 and E[X|Y] = ÷y+5, then the correlation…
A: Suppose X and Y are random variables with E(Y|X)⇒byx=-x+3E(X|Y)⇒bxy=14y+5 The required calculation…
Q: random sample of n1 = 10 regions in New England gave the following violent crime rates (per million…
A: We have used the excel data analysis tool to run the regression analysis.
Q: A stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain, A, so…
A: Given that stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain,…
Q: Consider an M/M/1 queueing system. If λ = 6 per hour and μ = 8 per hour find the probability of at…
A:
Q: A random sample of n1 = 10 regions in New England gave the following violent crime rates (per…
A: Introduction: Assume that the crime rate in Region NE and Region RM are independent. Further, the…
Q: A random sample of n1 = 10 regions in New England gave the following violent crime rates (per…
A: given, n1=10, n2=12 where n1 is the violent crime rate in New England Crime rate x1 =…
Q: Let X be a binomial random variable. If E(X)=3 and V(X)=1.5, then p(X=2) equals
A: First we have to determine the parameters of Binomial distribution, n and p with the help of E(X)…
Q: Let X be a binomial random variable with parameters of 9 and 0.1. Let Y be a binomial random…
A: Given that X+Y=2 So, the possible pairs are (0,2), (1,1), (2,0) So,…
Step by step
Solved in 2 steps with 2 images
- You study a population and are interested in the proportionpthat has a certain characteristic. You are unaware that this proportion of the population isp=0.67. You have taken a random sample of sizen & 129of the population and determined that the proportion of the sample having the characteristic isp=0.73. His sample is Sample 1 in the following table. (In the table, Sample 1 is indicated by "M1", Sample 2 by "M2", and so on). (to) Based on Sample 1, plot the confidence intervals of80%and of95%for the population proportion. Use1,282for the critical value for the confidence interval of80%, and use1960 for the critical value for the confidence interval of95%. (If necessary, you can refer to a list of formulas.) • Write the upper limit and the lower limit on the graphs to indicate each confidence interval. Write the answers with two decimal places. • For the points ( ♦and ◆), write the population proportion,0.67. 0.47 0.47 80% confidence interval 0.65 X 0.84 0.84 0.47 0.47 95% confidence…Please answer page 143, 2.6.6.85% of tax returns have computational errors. This means that if we randomly select a tax return, there is a probability of 0.85 that the tax return will have at least one computational error. Whether one tax return has a computational error is independent of whether any other tax return has a computational error. John Jay, a new tax return auditor randomly selects tax returns for audit one after another. Let X = the number of tax returns selected until he selects the 1st return with computational errors. Let Y = the number of tax returns selected until he selects the 2nd return with computational errors. What is the probability that the 1st 3 tax returns selected have computational errors? What is the expected value of X? What is the variance of X? What is the probability that X > 3? What is the probability that X < 3? What is the probability that Y = 4? What is the probability that Y< 4?
- 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.Question 3: Discrete random variables Each bit transmitted through a channel has a 10% chance to be transmitted in error. Assume that the bits are transmitted independently. Let X denote the number of bits in error in the next 18 transmitted bits. Answer the following questions a) Find the probability that in the next 18 transmitted bits, at least 3 transmitted in error. b) Calculate the expected value, variance and standard deviation of X. c) Find the probability that X is within 1 standard deviation of its mean value.Suppose that in a certain small town it either rains or is sunny every day. A meteorologist notes that when it is sunny in this town, it will be sunny the next day with probability 0.3. If it rains, it will be sunny the next day with probability 0.4. Answer the following questions:
- A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.Find P(X = 3) if the mean of the Poisson random variable is A = 10. O 0.007567 O 0.004540 O 0.000067 0.271801
- Chapters: Normal and Exponential random variables. Q: There exist naturally occurring random variables that are neither discrete nor continuous. Suppose a group of people is waiting for one more person to arrive before starting a meeting. Suppose that the arrival time of the person is exponential with mean 4 minutes, and that the meeting will start either when the person arrives or after 5 minutes, whichever comes first. Let X denote the length of time the group waits before starting the meeting. - a. Find P(05. Suppose that a student attending a class has an infectuous disease. Suppose that with probability 1/2 she does not infect anybody, with probability 1/4 she infects exactly one other person, and with probability 1/4 she infects exactly two people. Let X be the number of people infected by this student. Calculate the expectation and the variance of X.What does the memoryless property refer to? An event cannot occur if it has already occured within a recent specified time period. The distribution of the time until an event does not depend on how much time has already passed. The occurrence of an event is independent of the number of times that event has already occurred. None of the above.