If a random variable X has the gamma distribution with a = 2 and ẞ= 1, find P(1.7
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- A normally distributed random variable X with variance o2=256 and P(X> 130)=0.9251. Then the mean of X is 498.64 106.96 -238.64 153.04Random samples of size n=10,000 are taken from a population whose mean is μ=500 and standard deviation σ=400. The mean and standard error of the sample mean () are respectively:Assume that women's weights are normally distributed with a mean given by μ=143 and a standard deviation given by σ=29 lb.If 1 woman is randomly selected, find the probabity that her weight is above 176
- The World Bank records the prevalence of HIV in countries around the world. According to their data, "Prevalence of HIV refers to the percentage of people ages 15 to 49 who are infected with HIV." In one country, the prevalence of HIV is 16.3%. Let X= the number of people you test until you find a person infected with HIV Part (a) Sketch a graph of the distribution of the discrete random variable X P(X=X) 0.25 0.20 0.10 0.05 0.00 P(X=X) 0.15 0.10 0.05 0.00H Part (c) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Part (d) P(X=X) 0.25 0.20 (i) standard deviation 0.10 0.05 0.00 O P(X=X) 0.15) 0.10 0.05 What is the probability that you must test 30 people to find one with HIV? (Round your answer to four decimal places.) 0.00 456789 10 11 12 13 What is the probability that you must ask sixteen people? (Round your answer to four decimal places.) Find the mean and standard deviation of the distribution of X. (Round your answers to four decimal places.) (1) mean J and K are independent events. P(J | K) =…The amount of gasoline in gallons sold by three different gas stations during one day is given by the independent random variables X1,X2, X3 each with a normal distribution. X1 has a mean μ1 =700 and standard deviation σ1 = 55; X2 has mean μ2 =700 and standard deviation σ2 = 65; X3 has mean μ3=900 and standard deviation σ3 = 100. Suppose the prices per gallon are $2.90, $3.00 and $3.10 for X1, X2, and X3 respectively. Find the probability that the combined revenue for a given day is less than $6000. Use the z-score table. Round answer to the nearest hundredth.Emissions of nitrogen oxides, which are major constituents of smog, can be modeled using a normal distribution. Let x denote the amount of this pollutant emitted (in parts per billion) by a randomly selected vehicle. Suppose the distribution of x can be described by a normal distribution with ? = 1.8 and ? = 0.4. A city wants to offer some sort of incentive to get the worst polluters off the road. What emission levels constitute the worst 10% of the vehicles? (Round your answer to four decimal places.)
- Let X be a random sample from Exp(e). a. Find the CRLB for variance of any estimator b. Find CSS. c. Find the UMVUE using (a) as estimator and (b) as CSS d. Is the estimator in (b) efficient? Show/Justify?Suppose X1 is normally distributed with a mean of 3 and standard deviation of 0.3. Suppose X2 is normally distributed with a mean of 5 and a standard deviation of 0.7. Also suppose X1 and X2 are independent. Consider the variable Y = 4X1– 2X2. The distribution of Y has mean and standard deviation 4.Let X1, X2,...Xn be a random sample from a Poisson distribution with variance 0. Find a sufficient estimator for 0 and an unbiased estimator for 0 based on the sufficient estimator.call Wn
- Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 62.0 kg and standard deviation ? = 9.0 kg. Suppose a doe that weighs less than 53 kg is considered undernourished. (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 59 kg. If the average weight is less than 59 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 70 does is less than 59 kg (assuming a healthy population)? (Round your answer to four decimal places.) Suppose park rangers captured, weighed, and released 70 does in December, and the average weight was x = 63.8 kg. Do you think the doe population is undernourished or not? Explain. A. Since the sample average is above the mean, it…Let X be a random variable with mean u= E(X) = 10.33 and variance o = 12.81. Determine: E{10- E 10- 4The amount of nicotine in a cigarette produced by a tobacco company is a random variable with mean 2.2 mg and standard deviation 0.3 mg. Taking 100 randomly chosen cigarettes, let X; denote the nicotine content of the ith cigarette for i = 1,..., 100, and let X = 100 Ei=1 X; be the sample mean of the nicotine content. 100 a. What is the variance of X? Var(X) = Approximate the probability that X is higher than 2.25 in terms of the standard normal random variable. (The answer is given in terms of 2.25, standardized by mean and standard deviation of X.) P(X> 2.25) = P(Z >
