If a random variable X has the gamma distribution with a = 2 and ẞ= 1, find P(1.7
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A: It is given that X be a random variable that follows a standard normal distribution (mean μ = 0 and…
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Q: Group size 35 Group size 65 Group size 24/24F 124 2 178 282 125 140| 140 90 100 111 121 89 144 177…
A: Note : Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…
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A: Given data, Group size 35 Group size 65 Group size 24/24F 91 91 79 101 144 84 109 177 126…
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A: given data μx = 11σx = 1we have to find mean and standard deviation for given variable y,v and w.
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A: Null hypothesis: H0: µ1=µ2. That is, the mean number of volunteer hours on average is equal for…
Q: 35 - 65 e 24 /24F 91 99 110 91 144 176 80 86 124
A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…
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Q: 2Y 0 Show that has a x² distribution with 2 degrees of freedom.
A: Mean =θ ,
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Q: endard deviation of th
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A: Thank you for posing these questions. Since there are multiple questions posted, we will answer…
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A: Significance level (alpha) = 0.09 We know that, If x is random variable from standard normal…
Q: Let X be a random variable with a mean of 50 and a variance of 64. Find: i. P(x< 52) ii. P(35 < X <…
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A: Given: μ=5.3α=0σ.1 n=9
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A: Mean ()=16Standard deviation ()=10.36Sample size(n)=60
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A: Solution-: We find such that,
Q: Suppose X be a normally distributed random variable with unknown mean μ and a standard deviation of…
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Q: Members of fraternities and sororities are required to volunteer for community service. Do…
A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…
Q: Suppose X is an exponential random variable, and E(X) = 2. Find the probability that X will be…
A: Given, μ=2 σ2=22 σ=2 Probability density function of x is, p(X=x)=12e-x2…
Q: Find the F-test statistic to test the claim that the variances of the two populations are equal.…
A: Sample 1 S.D= s₁ = 2.1461 Sample 2 S.D= s₂ = 2.5122
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A: Given: μ = 7.5% σ = 2.0% x¯= 6.33% ∝ = 0.01 n = 19 The test hypothesis are, H0: μ = 7.5 H1: μ >…
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A: Given that, The original mean μ=41 and standard deviation σ=4 The standardized distribution mean…
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A: Suppose X is a normal random variable, and E(X) = 2.
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A: It is given that the mean and variance are 0 and 1.
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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) =…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.)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 WnLet 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- 4
- The 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 >Suppose X is a random variable of a normal distribution with E(X)=2 and Var(X)=4. Find P(X<4)Find the approximate mean and variance of Y = √X, where X is a randomvariable following a Poisson distribution.
