Let X be a random variable having a uniform distribution on the interval [0; 8]. Find the probability that X falls into interval (1; 7) at least eight times in ten experiments.
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Let X be a random variable having a uniform distribution on the interval [0; 8]. Find the probability that X falls into interval (1; 7) at least eight times in ten experiments.
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- For the X random variable known to have a Fuzzy Normal Distribution the parameters belonging to the distribution are the triangle with u = (12,17,18) and &2 = (4,5,9) %3D are fuzzy numbers. For this random variable, the fuzzy probability of P [13,16.5] Calculate for a= 0.19Suppose that X1,X2,...,X200 is a set of independent and identically distributed Gamma random variables with parameters α = 4,λ = 3. Describe the normal distribution that would correspond to the sum of those 200 random variables if the Central Limit Theorem holds.Let the random variable X be the number of months that a certain owner of an estate needs to pay a loan in the Bank if he/she has a contract with insurance company to help him/her to pay a loan. Say X has the p.m.f f(x) = x = 1,2,3,4 5-x 10' If the owner of an estate is to receive from an insurance company $200 for each of the first two months in the Bank and $100 for each month after the first tw what is the expected payment for the loan in the Bank?
- 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…Let the random variable X follows binomial distribution with parameters 14 and 5/12. Find P(X greater than 12).If the random variable X has a normal distribution with mean = 48 and standard deviation = 18, then P(1.2 ≤ X ≤ 4.8) is...
- The probability that data are entered incorrectly into a field in a database is 0.008. A data entry form has 24 fields, and errors occur independently for each field. The random variable X is the number of fields on the form with an error. Does X have a discrete uniform distribution? Why or why not?Suppose the time it takes my daugther, Lizzie, to eat an apple is uniformly distributed between 6 and 10 minutes. Let X = the time, in minutes, it takes Lizzie to eat an apple. What is the probability that it takes Lizzie more than 11 minutes to finish the next apple? What is the probability that it takes Lizzie at least 7.2 minutes to finish the next apple? What is the probability that it takes Lizzie fewer than 6.3 minutes or more than 8 minutes to finish the next apple?Let X1,X2,.,X, be a random sample from f(x;8) = 0e-8xIq0,c0) (x). Find a 100y or (1 - a)100 percent confidence interval for the mean of the population.
- Suppose a random variable X following χk2. Describe the distribution of X/k when k is large enough.Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are rolled. Find P(X = 12). (Round your answer to two decimal places.)4. Let X₁ N (0,3²), X₂ N(4,4²), and X3 ~ N(-1,22) be independent random variables. Find P (X₁ + X₂ +3X3 <-8), using the table for standard normal distribution.
