Let X1, X2, ..., Xn be a random sample from a Uniform(0,0 + 1) population with 0 > 0, *(3)**(3+1) X +X, where n is an even integer. Let M = be the median of the random sample. Find the probability density function of the median M. Find the expected value and variance of M.
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- If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recordedIf Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?Suppose 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.
- Consider a continuous random variable X such that P (−1 ≤ X ≤ 1) = 1/2. Can X be characterized by i) Uniform, and ii) Exponential distributions? If yes, find the distribution parameters which ensure the required property for X .Let X be a random variable that indicates the charging time of a battery. The probability density function is as in the picture. If the battery is known to charge in more than 2 hours, the probability that it will be less than 4 hours?