The probability distribution of a discrete random variable X is given below. Value x of X P(X=x) -1 0.26 0.18 1 0.15 0.29 3 0.12 Let Fy be the cumulative distribution function of X. Compute the following. (a) F (0) = 0.44 ? %3D (b) F (1) - F (-1) = 0.18 %3D

A random variable T follows Exponential distribution. Which of the following expression shows the Memoryless property of Exponential Distribution (choose the most appropriate answer): a). P(T > t + s| T < s) = P(T > t) b). P(T < t + s| T > s) = P(T < t) c). P(T < t + s| T > s) = P(T < s) d). Both a) and b)

Suppose that X and Y have the joint probability distribution shown to the right. (a) Find the marginal distribution of X. (b) Find the marginal distribution of Y. y f(x,y) 2 X 4 1 0.022 0.198 35 3 0.05 0.45 5 0.028 0.252

Linearity of expectations. A class with 11 third graders and 9 fourth graders are lined up in a random order for recess. T is the random variable which is equal to the number of 3rd graders in the first 3 places of the line. What is the expected value of T? E[T] = Ex: 1.23

The pdf of a random variable X is given by: f(x) = 0.2e-0.2x for x > 0 Please find P(x < 1). 0.4512 0.3297 0.8187 0.1813