A random variable x has a probability density π πχ 1 = {i ces + 8 0 Find the following a) mean value b) second moment c) variance fx(x)=16 2≤x≤6 elsewhere
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- 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 u = 57.0 kg and standard deviation o = 7.9 kg. Suppose a doe that weighs less than 48 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2350 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) does (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 55 does should be more than 54 kg. If the average weight is less than 54 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average welght x for a random sample of 55 does is less than…9. The random variable X is an equal mixture of 2 distributions: a gamma with a = a Pareto with a = 3, 0 = 1, 0 1000 %3D 2000 Calculate: The probability that X is less than it mean The mean and standard deviation of X a. b.2. Let X be a rs from a distribution with known variance o² and unknown mean 8. Find a (1a) CI for 0. Assume n is large.
- Assume the random variablex is normally distributed with mean u= 86 and standard deviation o = 4. Find the indicated probability. P(x<79) P(x<79)%3D P(x<79) =(Round to four decimal places as needed.)Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)This is a Statistics problem. Are the random variables Z1+Z2 and Z1-Z2 the same? Do they have the same distribution?
- certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with rate = 0.5 and shape parameter=4. If the daily capacity of that city is 8 million liters of water, what is the probability that on any given day the water supply is more than the daily capacity? O 0.174 O 0.5665 O 0434 O 0.8264Suppose the random variable X follows a normal distribution with mean 80 and variance 100. Then the probability is 0.6826 that X is in the symmetric interval about the mean between two numbers are A) -2 to 2 B) -3 to 3 C) -1 to 1 D) noneWeights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.
- Show full answers and steps to this exercise Please don’t use R or excel formula to calculate E(X) and variance. Use normal formula to get to the numbersThe random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630