document.write( "Question 874804: PROBABILITY DISTRIBUTIONS (Binomial and Poisson)\r \n" );
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document.write( "ABC company estimates the net profit on a new product ,that it is launching, to be Rs. 30,00,000 if it is successful, Rs. 10,00,000 if it is moderately successful and a loss of Rs. 10,00,000 if it is unsuccessful. The firm assigns the following probabilities to the different possibilities: Successful 0.15, moderately successful 0.25 and unsuccessful 0.60. Find the expected value and variance of the net profits.\r \n" );
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document.write( "A survey conducted over last 25 years indicated that in 10 years the winter was mild, in 8 years it was cold and in the remaining 7 years it was very cold . A company sells 1,000 woolen coats in the mild cold year, 1,300 in a cold year and 2000 in a very cold year. You are required to find the yearly expected profit of the company if a woolen coat costs Rs. 173 and is sold to stores for Rs. 248,\r \n" );
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document.write( "A company introduces a new product in the market and expects to make a profit of Rs. 2.5 lacs during first year if the demand is ‘good’, Rs. 1.5 lacs if the demand is ‘moderate’ and a loss of Rs 1 lac if the demand is ‘poor’ . Market research studies indicate that the probabilities for the demand to be good and moderate are 0.2 and 0.5 respectively. Find the company’s expected profit and standard deviation. \r \n" );
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document.write( "Find the mean and variance of the following probability distribution:\r \n" );
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document.write( " X = x 0 1 2 3 4 5 \n" );
document.write( "P(X = x) 3α 4α 4α 2α 2α 1α \n" );
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document.write( "Consider a random variable with the following probability distributions: P(x=0) = 0.1, P(x=1) = 0.2,P(x=2)=0.3, Px=3)=0.3 and P(x=4) =0.1 \n" );
document.write( "Find P(x≤2) \n" );
document.write( "Find P(1\n" );
document.write( "Find P(x≥0) \n" );
document.write( "Find the expected value of X \n" );
document.write( "Find the standard deviation of x.\r \n" );
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document.write( "The following examples are experiments and their associated random variables . In each case identify the values the random variable can take on and state whether the random variable is discrete or continuous. \n" );
document.write( " Experiment Random variable \n" );
document.write( "Take a 20 question examination Number of questions answered correctly \n" );
document.write( "Observe cars arriving at a tollbooth \n" );
document.write( "For 1 hour Number of cars arriving at the tollbooth \n" );
document.write( "Audit 50 tax returns Number of returns containing errors \n" );
document.write( "Observe an employee’s work \n" );
document.write( "For 8 hours Number of nonproductive hours \n" );
document.write( "Weigh a shipment of goods Number of pounds \n" );
document.write( "Build a new Library Percentage of project completed after 6 months\r \n" );
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document.write( "Data were collected on the number of operating rooms in use at Tampa General Hospital over a 20-day period. On 3 of the days only 1 operating room was use; on 5 days ,2 were use; on 8 days, 3 were used; and on 4 days all 4 rooms were used. \n" );
document.write( "Use the relative frequency approach to construct a probability distribution for the number of operating rooms in use on any given day. \n" );
document.write( "Draw a graph of probability distribution \n" );
document.write( "Find the expectation and standard deviation.\r \n" );
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document.write( "Consider a binomial experiment with 2 trials and p = 0.4 \n" );
document.write( "Compute the probability of 1 success \n" );
document.write( "Compute f(0) \n" );
document.write( "Compute f(2) \n" );
document.write( "Find the probability of at least 1 success \n" );
document.write( "Find the expected value, variance, and standard deviation\r \n" );
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document.write( "When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found. \n" );
document.write( "Describe the conditions under which this situation would b e a binomial experiment. \n" );
document.write( "How many experimental outcomes yield 1 defect? \n" );
document.write( "Compute the probabilities associated with finding no defects, 1 defect, and 2 defects.\r \n" );
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document.write( "Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the warning. Assume that a particular detection system has a 0.90 probability of detection a missile attack. Answer the following questions . \n" );
document.write( "What is the probability that 1 detection system will detect an attack? \n" );
document.write( "If 2 detection systems are installed in the same area and operate independently, what is the probability that at least 1 one of the systems will detect the attack? \n" );
document.write( "If 3 systems are installed, what is the probability that at least one of the systems will detect the attack? \n" );
document.write( "Would you recommend that multiple detection systems be operated? Explain.\r \n" );
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document.write( "If a production unit is made up from 20 identical components and each component has a probability of 0.25 of being effective, what is the average number of defective components in a unit? Further, What is the probability that in a unit (i) less than 3 components are defective?(ii)exactly 3 components are defective.\r \n" );
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document.write( "There are 24 battery cells in a box containing 6 defective cells that are randomly mixed. A customer buys 3 cells. What is the probability that he gets one defective cell? \r \n" );
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document.write( "The average number of customer arrivals per minute at a super bazaar is 2. Find the probability that during one particular minute (i)exactly 3 customers will arrive, (ii)at the most two customers will arrive,(iii)at least one customer will arrive.\r \n" );
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document.write( "A car hire firm has two cars which it hire out every day. The number of demands for a car on each days is distributed as a Poisson variate with mean 1.5. Calculate the proportion of days on which neither car is used and proportion of days on which some demand is refused.\r \n" );
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document.write( "An executive makes, on an average, 5 telephone calls per hour at a cost which may be taken as Rs2 per call, determine the probability that in any hour the telephone calls’ cost (i) exceeds Rs 6,(ii)remains less than Rs.10\r \n" );
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document.write( "The number of accidents in a year attributed to taxi drivers in a city follows Poisson distribution with mean 3. Out of 1,000 taxi drivers, find approximately the number of drivers with (i)no accident in a year, (ii) more than 3 accidents in a year.\r \n" );
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document.write( "Suppose that we are concerned with the occurrence e of major defects in a section of highway one month after resurfacing. We assume that the probability of a defect is the same for any two intervals of equal length, and that the occurrence or nonoccurrence of a defect in any one interval is independent of the occurrence or nonoccurrence in any other interval. Suppose that major defect s occur at the average rate of two per mile. Find the probability that \n" );
document.write( "No major defects will occur in a particular 3-mile section of the highway. \n" );
document.write( "At least two major defects in a 3-mile section of the highway.\r \n" );
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document.write( "For a Binomial distribution mean = 12, variance = 10. Find the parameters of the distribution , Also find the probability that the variate takes non-zero value. \n" );
document.write( "For a Binomial variate with parameters n = 14 & p = 0.4, write down the p.m.f. , mean and S.D. \n" );
document.write( "In a throw of a die 5 or 6 is considered a success. Find the mean and variance of the number of successes and compute P ( x ≥ 3),if a die is thrown 6 times. \n" );
document.write( "If X follows binomial distribution with parameters 10 and 0.6. find (i) E(X-6) ii)E(X-6)/10 \n" );
document.write( "iii) E(X-6)2 \n" );
document.write( "On an average 1 in every 50 valves manufactured by a firm is substandard. If the valves are supplied in packets of 20 each, find the probability that the packets will contains at least one substandard valve.\r \n" );
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document.write( "In a poisson distribution P2) =4 P(3), find P(4), P(x<3) & moment coefficient of skewness and kurtosis. \n" );
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