A random variable X follows a discrete distribution with support x = {−1,0, 1,2,3} and probability mass function (PMF) tabulated below: Value Probability −1 1/4 0 1/8 1 2 1/6 ? 3 1/6 (a) What is the probability that X is nonnegative? (b) Given that X is nongenative, what is probability that X ≥ 2? = (c) Define Y X2. Determine the probability mass function (PMF) of Y. Compute E(Y) either by definition of expectation or by LOTUS (Law of the Unconscious Statistician).

Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.

Let X be a random variable with a uniform distribution over the interval [-3,6]. Determine the mean of X. [The answer should be a number rounded to five decimal places, don't use symbols such as %]

Let X be a random variable with a uniform distribution over the interval [-2 , 4]. Determine the mean of X. The answer should be a number rounded to five decimal places