Suppose that we have data y = (y₁, ... ,yn). Each data-point is assumed to be generated by a distribution with the following probability density function: p(y¡ | 4) = 24y¡ exp(−¥y?), y¡ ≥ 0, i = 1,...,n. The unknown parameter is , with > 0. Write down the likelihood for given y. Find an expression for the maximum likelihood estimate (MLE) .

Let X ~ Uniform(a, b). Find Expected value EX.

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?

Let the test statistic T have at distribution when H, is true. Give the P-value for each of the following situations. (Round your answers to three decimal places.) n USE SALT (a) H: u > Ho, df = 13, t = 2.663 P-value = (b) H3: µ < Ho, n = 27, t = 2.131 P-value = (c) H: u # Ho, n = 41, t = -1.581 or t = 1.581 P-value =

Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, o = 2.8, find a value xo that represents the 80th percentile of the distribution. Answer should be accurate to two decimal places.

Please answer both parts of the question thanks

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The time it takes me to ride my bike to school is uniformly distributed between 27 minutes and 36 minutes What is the probability that I can ride my bike to school in under 35 minutes? Give your answer accurate to two decimal places.

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