fx(x) = (0+1)xº, if 0 ≤ x ≤ 1; otherwise. 0, Find the maximum likelihood estimator of given i.i.d. samples X₁,..., Xn. 1,

The wait time at a popular fast food restaurant is uniformly distributed between 2 and 10 minutes on average (a) Find the probability that you wait less than 4 minutes.  (b) Find the probability that you wait between 8 and 10 minutes. (c) Explain why the answers to (a) and (b) are the same. Hint: draw the probability density function for a Uniform random variable. Explain with a graph and also without a graph.

Please explain the formula for Expected Value for Hypergeometric Distribution using an example

the driving time from toronto to montreal are uniformly distributed with times ranging from four hours to 5.75 hours. draw a probability density graph that shows this (be sure to fully label your graph).

Let Z be a st andard normal variable. Let mean and standard derviation > 0 be two real numbers. Then, the distribution of the random variableIs  X=emean+standard derviation*Z called the Lognorma (mean,standard derviation) distribution. Write a function to generate random variables from this Lognormal distribution using a transformation method and generate a random sample of size n = 1000. Compare the histogram with the lognormal density curve given by dlnorm function in R.

Question * Given X be the life time of a bulb having a probability density function f(x) =-e for x>0 and 0 elsewhere. The mean life time of the bulbs is equal to: %3D O 1/2 O None of these O 1/4 Question* Let X and Y be two independent continuous random variables with marginal distribution

Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?

9/10 Question * If the probability density function of random variable X is given by: - 1)(2- x), 0, 15 xS 2; otherwise. The value of k is equal to: None of these 3/2 7. 6. Question *