Consider a random variable X that follows a uniform distribution with a= 1 and b = 4 Find the expected value of X
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Consider a random variable X that follows a uniform distribution with a= 1 and b = 4
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- • The expected value of x is (enter an exact decimal in 0, 1). • The variance of x is (enter a decimal rounded to the third decimal place).REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adultst. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 8 children (9 years old) showed that they had an average REM sleep time of x, = 2.9 hours per night. From previous studies, it is known that o, = 0.6 hour. Another random sample of n, = 8 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that o, = 0.7 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 = H2i HiitHy> H2 O Ho: H,I need your help Thank youLet 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…I need help with dYou are to roll a fair die n=108 times, each time observing the number of dots appearing on the top side of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i=1,2,⋯,108. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die.μXi= ____________ Enter your answer using all the decimals you can.σXi= ____________ Enter your answer using all the decimals you can. (b) What is the probability that the average topside on your tosses will be somewhere between 3.4 and 3.7? Enter your answer using all the decimals you can. _____________ (c) What is the probability that the average of your tosses is greater than 4.15? Enter your answer using all the decimals you can. ______________Which is not an assumed characteristic of & in the population model y₁ = Be + B₁ X₁ + εi? Multiple Choice It is a random variable. It has zero mean. ○ It is a statistic. It is unobservable.Let X be a random variable with range {20,30,50} and probability distribution P(X=20) = 0.25,P(X=30) = 0.25, and P(X=50) = 0.5. What is the expected value of X?The probability of having a red color ball is 15%. The boy selected four submitted balls at random, let X be a random variable indicating the number of red color balls out of those balls selected by the boy. Identify and compute the expected value for the random variable X, i.e. E(X).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 ? = 55.0 kg and standard deviation ? = 8.4 kg. Suppose a doe that weighs less than 46 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 2850 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 = 40 does should be more than 52 kg. If the average weight is less than 52 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 40 does is less than…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 ? = 53.0 kg and standard deviation ? = 8.7 kg. Suppose a doe that weighs less than 44 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 2150 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 = 80 does should be more than 50 kg. If the average weight is less than 50 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 80 does is less…The joint distribution of the pair of random variables as given in the following table: 0 Y 1 2 -10 X 0 10 0.2 0.1 0 0.066 0.046 0.052 0.072 0.042 O No answer 0.1 0.2 0 0.1 0.1 0.2 A random sample of 4 is taken of the random variable X. What is pZX₁/425? 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