Suppose X is random variable with a generic distribution Fx (x) = G(x) Question 5 on (-∞, ∞). Define the new random variable Y = min [0, X]. Now, calculate, in terms of G(), the distribution Fy.

Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.

If a discrete random variable X has the following probability distribution: X      -2, - 1,     0,     1,      2 P(X) 0.2, 0.3, 0.15, 0.2,  0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!

Use the data in the table below, which shows the employment status of individuals in a particular town by age group. Part-time Unemployed Age Full-time 0-17 25 187 252 18-25 391 200 199 26-34 434 66 22 35-49 562 192 149 50+ 461 170 237 If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?